Grade 8 Algebra: Writing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Simple statements

1. Write an inequality:
$x\text{}$ $\text{is}$ $\text{greater}$ $\text{than}$ $\text{5}$
2. Write an inequality:
$y\text{}$ $\text{is}$ $\text{less}$ $\text{than}$ $\text{3}$
3. Write an inequality:
$n\text{}$ $\text{is}$ $\text{at}$ $\text{least}$ $\text{10}$
4. Write an inequality:
$m\text{}$ $\text{is}$ $\text{at}$ $\text{most}$ $\text{7}$
5. Write an inequality:
$k\text{}$ $\text{is}$ $\text{no}$ $\text{more}$ $\text{than}$ $\text{4}$
6. Write an inequality:
$p\text{}$ $\text{is}$ $\text{more}$ $\text{than}$ $\text{-2}$

Answer Key

Level 1

1. $x > 5$
2. $y < 3$
3. $n \ge 10$
4. $m \le 7$
5. $k \le 4$
6. $p > -2$

Grade 8 Algebra: Writing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Expressions with operations

1. Write an inequality:
$\text{twice}$ $\text{a}$ $\text{number}$ $x\text{}$ $\text{is}$ $\text{greater}$ $\text{than}$ $\text{12}$
2. Write an inequality:
$\text{a}$ $\text{number}$ $n\text{}$ $\text{plus}$ $\text{4}$ $\text{is}$ $\text{less}$ $\text{than}$ $\text{9}$
3. Write an inequality:
$\text{5}$ $\text{less}$ $\text{than}$ $y\text{}$ $\text{is}$ $\text{at}$ $\text{least}$ $\text{8}$
4. Write an inequality:
$\text{the}$ $\text{quotient}$ $\text{of}$ $m\text{}$ $\text{and}$ $\text{3}$ $\text{is}$ $\text{at}$ $\text{most}$ $\text{6}$
5. Write an inequality:
$\text{3}$ $\text{times}$ $k\text{,}$ $\text{minus}$ $\text{1,}$ $\text{is}$ $\text{greater}$ $\text{than}$ $\text{11}$
6. Write an inequality:
$\text{half}$ $\text{of}$ $p\text{}$ $\text{is}$ $\text{no}$ $\text{less}$ $\text{than}$ $\text{4}$

Answer Key

Level 2

1. $2x > 12$
2. $n + 4 < 9$
3. $y - 5 \ge 8$
4. $\dfrac{m}{3} \le 6$
5. $3k - 1 > 11$
6. $\tfrac{1}{2}p \ge 4$

Grade 8 Algebra: Writing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Real-life situations

1. Write an inequality:
$\text{You}$ $\text{must}$ $\text{be}$ $\text{at}$ $\text{least}$ $\text{48}$ $\text{inches}$ $\text{tall}$ $\text{to}$ $\text{ride.}$ $\text{Use}$ $h\text{}$ $\text{for}$ $\text{height.}$
2. Write an inequality:
$\text{A}$ $\text{bag}$ $\text{can}$ $\text{hold}$ $\text{at}$ $\text{most}$ $\text{20}$ $\text{pounds.}$ $\text{Use}$ $w\text{}$ $\text{for}$ $\text{weight.}$
3. Write an inequality:
$\text{The}$ $\text{speed}$ $\text{limit}$ $\text{is}$ $\text{65}$ $\text{miles}$ $\text{per}$ $\text{hour.}$ $\text{Your}$ $\text{speed}$ $s\text{}$ $\text{cannot}$ $\text{be}$ $\text{more.}$
4. Write an inequality:
$\text{Tickets}$ $\text{cost}$ $\text{8}$ $\text{dollars}$ $\text{each}$ $\text{and}$ $\text{you}$ $\text{have}$ $\text{50}$ $\text{dollars.}$ $\text{Use}$ $t\text{}$ $\text{for}$ $\text{tickets.}$
5. Write an inequality:
$\text{You}$ $\text{want}$ $\text{to}$ $\text{earn}$ $\text{more}$ $\text{than}$ $\text{100}$ $\text{dollars}$ $\text{at}$ $\text{12}$ $\text{dollars}$ $\text{per}$ $\text{hour.}$ $\text{Use}$ $h\text{}$ $\text{for}$ $\text{hours.}$
6. Write an inequality:
$\text{A}$ $\text{plan}$ $\text{costs}$ $\text{20}$ $\text{dollars}$ $\text{plus}$ $\text{5}$ $\text{dollars}$ $\text{per}$ $\text{GB}$ $g\text{,}$ $\text{and}$ $\text{must}$ $\text{stay}$ $\text{under}$ $\text{45}$ $\text{dollars.}$

Answer Key

Level 3

1. $h \ge 48$
2. $w \le 20$
3. $s \le 65$
4. $8t \le 50$
5. $12h > 100$
6. $20 + 5g < 45$

Grade 8 Algebra: One-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Addition and subtraction

1. Solve:
$x + 4 > 9$
2. Solve:
$y - 3 \le 7$
3. Solve:
$n + 8 < 2$
4. Solve:
$m - 5 \ge -1$
5. Solve:
$6 + k > 15$
6. Solve:
$p - 2.5 < 1.5$

Answer Key

Level 1

1. $x > 5$
2. $y \le 10$
3. $n < -6$
4. $m \ge 4$
5. $k > 9$
6. $p < 4$

Grade 8 Algebra: One-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Multiply or divide by a positive

1. Solve:
$3x < 18$
2. Solve:
$\dfrac{y}{4} \ge 5$
3. Solve:
$7n > -21$
4. Solve:
$\dfrac{m}{2} \le -3$
5. Solve:
$5k \ge 35$
6. Solve:
$\tfrac{2}{3}p < 8$

Answer Key

Level 2

1. $x < 6$
2. $y \ge 20$
3. $n > -3$
4. $m \le -6$
5. $k \ge 7$
6. $p < 12$

Grade 8 Algebra: One-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Multiply or divide by a negative (flip the sign)

1. Solve:
$-2x < 10$
2. Solve:
$-\dfrac{y}{3} \ge 4$
3. Solve:
$-5n \le -25$
4. Solve:
$\dfrac{m}{-4} > 2$
5. Solve:
$-k > 6$
6. Solve:
$-0.5p \ge 3$

Answer Key

Level 3

1. $x > -5$
2. $y \le -12$
3. $n \ge 5$
4. $m < -8$
5. $k < -6$
6. $p \le -6$

Grade 8 Algebra: Two-Step and Multi-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Two-step, positive coefficients

1. Solve:
$2x + 3 > 11$
2. Solve:
$3y - 4 \le 14$
3. Solve:
$4n + 1 < -7$
4. Solve:
$5m - 2 \ge 13$
5. Solve:
$\dfrac{k}{2} + 1 > 4$
6. Solve:
$6p + 5 \le 35$

Answer Key

Level 1

1. $x > 4$
2. $y \le 6$
3. $n < -2$
4. $m \ge 3$
5. $k > 6$
6. $p \le 5$

Grade 8 Algebra: Two-Step and Multi-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Two-step, flip the sign

1. Solve:
$-3x + 2 > 14$
2. Solve:
$5 - 2y \le 11$
3. Solve:
$-4n - 1 < 15$
4. Solve:
$7 - m \ge 3$
5. Solve:
$-\dfrac{k}{2} + 3 < 1$
6. Solve:
$10 - 3p > -5$

Answer Key

Level 2

1. $x < -4$
2. $y \ge -3$
3. $n > -4$
4. $m \le 4$
5. $k > 4$
6. $p < 5$

Grade 8 Algebra: Two-Step and Multi-Step Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Distribute and variables on both sides

1. Solve:
$3(x - 2) > 9$
2. Solve:
$2(y + 4) \le 3y + 1$
3. Solve:
$5n - 3 < 2n + 9$
4. Solve:
$-2(m - 1) \ge m + 8$
5. Solve:
$4(k + 1) - k > 16$
6. Solve:
$\dfrac{p + 5}{3} < p - 1$

Answer Key

Level 3

1. $x > 5$
2. $y \ge 7$
3. $n < 4$
4. $m \le -2$
5. $k > 4$
6. $p > 4$

Grade 8 Algebra: Word Problems: Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 1

One-step situations

1. Write an inequality and solve:
$\text{Sara}$ $\text{has}$ $\text{15}$ $\text{dollars.}$ $\text{She}$ $\text{wants}$ $\text{at}$ $\text{least}$ $\text{40}$ $\text{dollars.}$ $\text{How}$ $\text{much}$ $\text{more}$ $\text{money}$ $m\text{}$ $\text{does}$ $\text{she}$ $\text{need?}$
2. Write an inequality and solve:
$\text{A}$ $\text{van}$ $\text{holds}$ $\text{at}$ $\text{most}$ $\text{12}$ $\text{people}$ $\text{and}$ $\text{5}$ $\text{are}$ $\text{already}$ $\text{in.}$ $\text{How}$ $\text{many}$ $\text{more}$ $\text{people}$ $p\text{}$ $\text{can}$ $\text{get}$ $\text{in?}$
3. Write an inequality and solve:
$\text{Each}$ $\text{book}$ $\text{costs}$ $\text{6}$ $\text{dollars.}$ $\text{Ali}$ $\text{has}$ $\text{42}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{books}$ $b\text{}$ $\text{can}$ $\text{he}$ $\text{buy?}$
4. Write an inequality and solve:
$\text{A}$ $\text{plant}$ $\text{must}$ $\text{grow}$ $\text{more}$ $\text{than}$ $\text{9}$ $\text{cm.}$ $\text{It}$ $\text{has}$ $\text{grown}$ $\text{4}$ $\text{cm.}$ $\text{How}$ $\text{much}$ $\text{more}$ $\text{growth}$ $g\text{}$ $\text{is}$ $\text{needed?}$
5. Write an inequality and solve:
$\text{Pens}$ $\text{cost}$ $\text{2}$ $\text{dollars}$ $\text{each.}$ $\text{Spend}$ $\text{less}$ $\text{than}$ $\text{15}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{pens}$ $n\text{}$ $\text{can}$ $\text{you}$ $\text{buy?}$
6. Write an inequality and solve:
$\text{A}$ $\text{team}$ $\text{needs}$ $\text{more}$ $\text{than}$ $\text{30}$ $\text{points}$ $\text{and}$ $\text{has}$ $\text{18.}$ $\text{How}$ $\text{many}$ $\text{more}$ $\text{points}$ $p\text{}$ $\text{do}$ $\text{they}$ $\text{need?}$

Answer Key

Level 1

1. $15 + m \ge 40,\; m \ge 25$
2. $5 + p \le 12,\; p \le 7$
3. $6b \le 42,\; b \le 7$
4. $4 + g > 9,\; g > 5$
5. $2n < 15,\; n < 7.5 \;(\text{at most } 7)$
6. $18 + p > 30,\; p > 12$

Grade 8 Algebra: Word Problems: Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Two-step situations

1. Write an inequality and solve:
$\text{A}$ $\text{gym}$ $\text{costs}$ $\text{20}$ $\text{dollars}$ $\text{to}$ $\text{join}$ $\text{plus}$ $\text{15}$ $\text{dollars}$ $\text{per}$ $\text{month.}$ $\text{The}$ $\text{budget}$ $\text{is}$ $\text{at}$ $\text{most}$ $\text{110}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{months}$ $m\text{?}$
2. Write an inequality and solve:
$\text{A}$ $\text{taxi}$ $\text{charges}$ $\text{4}$ $\text{dollars}$ $\text{plus}$ $\text{2}$ $\text{dollars}$ $\text{per}$ $\text{mile.}$ $\text{You}$ $\text{can}$ $\text{spend}$ $\text{at}$ $\text{most}$ $\text{20}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{miles}$ $m\text{?}$
3. Write an inequality and solve:
$\text{Kim}$ $\text{has}$ $\text{50}$ $\text{dollars}$ $\text{and}$ $\text{spends}$ $\text{7}$ $\text{dollars}$ $\text{per}$ $\text{week.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{weeks}$ $w\text{}$ $\text{will}$ $\text{she}$ $\text{have}$ $\text{less}$ $\text{than}$ $\text{15}$ $\text{dollars?}$
4. Write an inequality and solve:
$\text{Cookies}$ $\text{sell}$ $\text{for}$ $\text{3}$ $\text{dollars}$ $\text{each}$ $\text{and}$ $\text{supplies}$ $\text{cost}$ $\text{24}$ $\text{dollars.}$ $\text{The}$ $\text{profit}$ $\text{must}$ $\text{be}$ $\text{at}$ $\text{least}$ $\text{60}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{cookies}$ $c\text{?}$
5. Write an inequality and solve:
$\text{A}$ $\text{phone}$ $\text{plan}$ $\text{costs}$ $\text{30}$ $\text{dollars}$ $\text{plus}$ $\text{0.10}$ $\text{dollars}$ $\text{per}$ $\text{text.}$ $\text{Keep}$ $\text{the}$ $\text{bill}$ $\text{under}$ $\text{45}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{texts}$ $t\text{?}$
6. Write an inequality and solve:
$\text{A}$ $\text{pool}$ $\text{has}$ $\text{120}$ $\text{liters}$ $\text{and}$ $\text{fills}$ $\text{at}$ $\text{40}$ $\text{liters}$ $\text{per}$ $\text{minute.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{minutes}$ $m\text{}$ $\text{will}$ $\text{it}$ $\text{have}$ $\text{at}$ $\text{least}$ $\text{400}$ $\text{liters?}$

Answer Key

Level 2

1. $20 + 15m \le 110,\; m \le 6$
2. $4 + 2m \le 20,\; m \le 8$
3. $50 - 7w < 15,\; w > 5$
4. $3c - 24 \ge 60,\; c \ge 28$
5. $30 + 0.1t < 45,\; t < 150$
6. $120 + 40m \ge 400,\; m \ge 7$

Grade 8 Algebra: Word Problems: Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Comparisons and averages

1. Write an inequality and solve:
$\text{Plan}$ $\text{1}$ $\text{costs}$ $\text{25}$ $\text{dollars}$ $\text{plus}$ $\text{3}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{Plan}$ $\text{2}$ $\text{costs}$ $\text{7}$ $\text{dollars}$ $\text{per}$ $\text{visit.}$ $\text{For}$ $\text{how}$ $\text{many}$ $\text{visits}$ $v\text{}$ $\text{is}$ $\text{Plan}$ $\text{1}$ $\text{cheaper?}$
2. Write an inequality and solve:
$\text{A}$ $\text{rectangle}$ $\text{has}$ $\text{width}$ $w\text{}$ $\text{and}$ $\text{its}$ $\text{length}$ $\text{is}$ $\text{twice}$ $\text{the}$ $\text{width.}$ $\text{Its}$ $\text{perimeter}$ $\text{is}$ $\text{at}$ $\text{most}$ $\text{36}$ $\text{cm.}$ $\text{Find}$ $\text{the}$ $\text{possible}$ $\text{widths.}$
3. Write an inequality and solve:
$\text{Leo}$ $\text{earns}$ $\text{8}$ $\text{dollars}$ $\text{per}$ $\text{hour}$ $\text{plus}$ $\text{a}$ $\text{20}$ $\text{dollar}$ $\text{bonus.}$ $\text{He}$ $\text{wants}$ $\text{more}$ $\text{than}$ $\text{100}$ $\text{dollars.}$ $\text{How}$ $\text{many}$ $\text{hours}$ $h\text{?}$
4. Write an inequality and solve:
$\text{The}$ $\text{sum}$ $\text{of}$ $\text{three}$ $\text{consecutive}$ $\text{integers}$ $\text{is}$ $\text{less}$ $\text{than}$ $\text{60.}$ $\text{What}$ $\text{is}$ $\text{the}$ $\text{largest}$ $\text{possible}$ $\text{smallest}$ $\text{integer}$ $n\text{?}$
5. Write an inequality and solve:
$\text{Test}$ $\text{scores}$ $\text{are}$ $\text{82}$ $\text{and}$ $\text{90.}$ $\text{The}$ $\text{average}$ $\text{of}$ $\text{three}$ $\text{tests}$ $\text{must}$ $\text{be}$ $\text{at}$ $\text{least}$ $\text{85.}$ $\text{What}$ $\text{third}$ $\text{score}$ $s\text{}$ $\text{is}$ $\text{needed?}$
6. Write an inequality and solve:
$\text{Mia}$ $\text{has}$ $\text{200}$ $\text{dollars}$ $\text{and}$ $\text{spends}$ $\text{15}$ $\text{dollars}$ $\text{per}$ $\text{week.}$ $\text{Tom}$ $\text{has}$ $\text{80}$ $\text{dollars}$ $\text{and}$ $\text{saves}$ $\text{10}$ $\text{dollars}$ $\text{per}$ $\text{week.}$ $\text{After}$ $\text{how}$ $\text{many}$ $\text{weeks}$ $w\text{}$ $\text{does}$ $\text{Tom}$ $\text{have}$ $\text{more?}$

Answer Key

Level 3

1. $25 + 3v < 7v,\; v > 6.25 \;(\text{7 or more})$
2. $6w \le 36,\; w \le 6$
3. $8h + 20 > 100,\; h > 10$
4. $3n + 3 < 60,\; n < 19 \;(n = 18)$
5. $\dfrac{82 + 90 + s}{3} \ge 85,\; s \ge 83$
6. $80 + 10w > 200 - 15w,\; w > 4.8 \;(\text{5 weeks})$

Grade 8 Algebra: Number Lines: Reading and Graphing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Read the graph

1. Write the inequality shown on the number line:
2. Write the inequality shown on the number line:
3. Write the inequality shown on the number line:
4. Write the inequality shown on the number line:
5. Write the inequality shown on the number line:
6. Write the inequality shown on the number line:

Answer Key

Level 1

1. $x > 3$
2. $x \le -2$
3. $x \ge 0$
4. $x < 5$
5. $x > -4$
6. $x \le 1$

Grade 8 Algebra: Number Lines: Reading and Graphing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Graph the inequality

1. Graph on the number line:
$x < 4$
2. Graph on the number line:
$x \ge -3$
3. Graph on the number line:
$x > -1$
4. Graph on the number line:
$x \le 2$
5. Graph on the number line:
$3 \ge x$
6. Graph on the number line:
$-2 < x$

Answer Key

Level 2

1. $\text{open circle at } 4\text{, shade left}$
2. $\text{closed circle at } -3\text{, shade right}$
3. $\text{open circle at } -1\text{, shade right}$
4. $\text{closed circle at } 2\text{, shade left}$
5. $\text{closed circle at } 3\text{, shade left}$
6. $\text{open circle at } -2\text{, shade right}$

Grade 8 Algebra: Number Lines: Reading and Graphing Inequalities

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Solve, then graph

1. Solve, then graph on the number line:
$2x + 1 > 7$
2. Solve, then graph on the number line:
$-3x \le 9$
3. Solve, then graph on the number line:
$\dfrac{x}{2} - 1 < 1$
4. Solve, then graph on the number line:
$5 - x \ge 2$
5. Solve, then graph on the number line:
$3x - 4 \le -10$
6. Solve, then graph on the number line:
$-2x + 5 < 1$

Answer Key

Level 3

1. $x > 3,\; \text{open circle at } 3\text{, shade right}$
2. $x \ge -3,\; \text{closed circle at } -3\text{, shade right}$
3. $x < 4,\; \text{open circle at } 4\text{, shade left}$
4. $x \le 3,\; \text{closed circle at } 3\text{, shade left}$
5. $x \le -2,\; \text{closed circle at } -2\text{, shade left}$
6. $x > 2,\; \text{open circle at } 2\text{, shade right}$