← Back to Topic 2

Linear Equations: Classroom Packet

Grade 8 Algebra: One-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Addition and subtraction

  1. 1. Solve:
    x+6=14x + 6 = 14
  2. 2. Solve:
    y−9=4y - 9 = 4
  3. 3. Solve:
    n+15=22n + 15 = 22
  4. 4. Solve:
    m−7=0m - 7 = 0
  5. 5. Solve:
    12+k=3012 + k = 30
  6. 6. Solve:
    p−3=11p - 3 = 11

Answer Key

Level 1

  1. 1. x=8x = 8
  2. 2. y=13y = 13
  3. 3. n=7n = 7
  4. 4. m=7m = 7
  5. 5. k=18k = 18
  6. 6. p=14p = 14

Grade 8 Algebra: One-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Multiplication and division

  1. 1. Solve:
    5x=355x = 35
  2. 2. Solve:
    y3=6\dfrac{y}{3} = 6
  3. 3. Solve:
    8n=648n = 64
  4. 4. Solve:
    m7=4\dfrac{m}{7} = 4
  5. 5. Solve:
    9k=549k = 54
  6. 6. Solve:
    p5=12\dfrac{p}{5} = 12

Answer Key

Level 2

  1. 1. x=7x = 7
  2. 2. y=18y = 18
  3. 3. n=8n = 8
  4. 4. m=28m = 28
  5. 5. k=6k = 6
  6. 6. p=60p = 60

Grade 8 Algebra: One-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Negatives, fractions and decimals

  1. 1. Solve:
    x+8=−3x + 8 = -3
  2. 2. Solve:
    −4y=28-4y = 28
  3. 3. Solve:
    n−2=9\dfrac{n}{-2} = 9
  4. 4. Solve:
    23m=10\tfrac{2}{3}m = 10
  5. 5. Solve:
    0.5k=4.50.5k = 4.5
  6. 6. Solve:
    p−2.7=−1.3p - 2.7 = -1.3

Answer Key

Level 3

  1. 1. x=−11x = -11
  2. 2. y=−7y = -7
  3. 3. n=−18n = -18
  4. 4. m=15m = 15
  5. 5. k=9k = 9
  6. 6. p=1.4p = 1.4

Grade 8 Algebra: Two-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Whole numbers

  1. 1. Solve:
    2x+3=112x + 3 = 11
  2. 2. Solve:
    3y−5=163y - 5 = 16
  3. 3. Solve:
    4n+1=254n + 1 = 25
  4. 4. Solve:
    5m−10=155m - 10 = 15
  5. 5. Solve:
    6k+4=406k + 4 = 40
  6. 6. Solve:
    7p−2=477p - 2 = 47

Answer Key

Level 1

  1. 1. x=4x = 4
  2. 2. y=7y = 7
  3. 3. n=6n = 6
  4. 4. m=5m = 5
  5. 5. k=6k = 6
  6. 6. p=7p = 7

Grade 8 Algebra: Two-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Negatives and division

  1. 1. Solve:
    −3x+4=19-3x + 4 = 19
  2. 2. Solve:
    y4−2=3\dfrac{y}{4} - 2 = 3
  3. 3. Solve:
    −2n−7=5-2n - 7 = 5
  4. 4. Solve:
    m3+5=−1\dfrac{m}{3} + 5 = -1
  5. 5. Solve:
    8−3k=238 - 3k = 23
  6. 6. Solve:
    p+42=9\dfrac{p + 4}{2} = 9

Answer Key

Level 2

  1. 1. x=−5x = -5
  2. 2. y=20y = 20
  3. 3. n=−6n = -6
  4. 4. m=−18m = -18
  5. 5. k=−5k = -5
  6. 6. p=14p = 14

Grade 8 Algebra: Two-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Fractions and decimals

  1. 1. Solve:
    12x+3=8\tfrac{1}{2}x + 3 = 8
  2. 2. Solve:
    34y−1=5\tfrac{3}{4}y - 1 = 5
  3. 3. Solve:
    0.2n+1.5=3.50.2n + 1.5 = 3.5
  4. 4. Solve:
    2m−15=3\dfrac{2m - 1}{5} = 3
  5. 5. Solve:
    −23k+4=10-\tfrac{2}{3}k + 4 = 10
  6. 6. Solve:
    1.5p−0.5=41.5p - 0.5 = 4

Answer Key

Level 3

  1. 1. x=10x = 10
  2. 2. y=8y = 8
  3. 3. n=10n = 10
  4. 4. m=8m = 8
  5. 5. k=−9k = -9
  6. 6. p=3p = 3

Grade 8 Algebra: Multi-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Combine like terms first

  1. 1. Solve:
    3x+2x=253x + 2x = 25
  2. 2. Solve:
    4y+3−y=184y + 3 - y = 18
  3. 3. Solve:
    7n−2n+1=217n - 2n + 1 = 21
  4. 4. Solve:
    2m+5+3m=302m + 5 + 3m = 30
  5. 5. Solve:
    6k−4−2k=126k - 4 - 2k = 12
  6. 6. Solve:
    9p−3p−6=309p - 3p - 6 = 30

Answer Key

Level 1

  1. 1. x=5x = 5
  2. 2. y=5y = 5
  3. 3. n=4n = 4
  4. 4. m=5m = 5
  5. 5. k=4k = 4
  6. 6. p=6p = 6

Grade 8 Algebra: Multi-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Distributive property

  1. 1. Solve:
    2(x+4)=182(x + 4) = 18
  2. 2. Solve:
    3(y−2)=213(y - 2) = 21
  3. 3. Solve:
    −4(n+1)=12-4(n + 1) = 12
  4. 4. Solve:
    5(2m−1)=355(2m - 1) = 35
  5. 5. Solve:
    12(k+6)=7\tfrac{1}{2}(k + 6) = 7
  6. 6. Solve:
    −(p−3)=8-(p - 3) = 8

Answer Key

Level 2

  1. 1. x=5x = 5
  2. 2. y=9y = 9
  3. 3. n=−4n = -4
  4. 4. m=4m = 4
  5. 5. k=8k = 8
  6. 6. p=−5p = -5

Grade 8 Algebra: Multi-Step Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Distribute and combine

  1. 1. Solve:
    3(x+2)+4=223(x + 2) + 4 = 22
  2. 2. Solve:
    2(y−3)+5y=152(y - 3) + 5y = 15
  3. 3. Solve:
    4(n+1)−2(n−3)=164(n + 1) - 2(n - 3) = 16
  4. 4. Solve:
    5−2(m+4)=−95 - 2(m + 4) = -9
  5. 5. Solve:
    3(2k−1)−(k+2)=203(2k - 1) - (k + 2) = 20
  6. 6. Solve:
    13(6p−9)+p=9\tfrac{1}{3}(6p - 9) + p = 9

Answer Key

Level 3

  1. 1. x=4x = 4
  2. 2. y=3y = 3
  3. 3. n=3n = 3
  4. 4. m=3m = 3
  5. 5. k=5k = 5
  6. 6. p=4p = 4

Grade 8 Algebra: Variables on Both Sides

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Simple both-sides

  1. 1. Solve:
    5x=3x+85x = 3x + 8
  2. 2. Solve:
    7y−4=3y+127y - 4 = 3y + 12
  3. 3. Solve:
    2n+9=5n2n + 9 = 5n
  4. 4. Solve:
    6m+1=4m+116m + 1 = 4m + 11
  5. 5. Solve:
    9k−5=4k+209k - 5 = 4k + 20
  6. 6. Solve:
    3p+14=8p−13p + 14 = 8p - 1

Answer Key

Level 1

  1. 1. x=4x = 4
  2. 2. y=4y = 4
  3. 3. n=3n = 3
  4. 4. m=5m = 5
  5. 5. k=5k = 5
  6. 6. p=3p = 3

Grade 8 Algebra: Variables on Both Sides

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Distribute first

  1. 1. Solve:
    2(x+3)=x+102(x + 3) = x + 10
  2. 2. Solve:
    4(y−1)=2y+64(y - 1) = 2y + 6
  3. 3. Solve:
    3(n+2)=5(n−2)3(n + 2) = 5(n - 2)
  4. 4. Solve:
    −2(m−4)=m−7-2(m - 4) = m - 7
  5. 5. Solve:
    6(k+1)=2(k+9)6(k + 1) = 2(k + 9)
  6. 6. Solve:
    5(p−2)=3p+45(p - 2) = 3p + 4

Answer Key

Level 2

  1. 1. x=4x = 4
  2. 2. y=5y = 5
  3. 3. n=8n = 8
  4. 4. m=5m = 5
  5. 5. k=3k = 3
  6. 6. p=7p = 7

Grade 8 Algebra: Variables on Both Sides

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Special cases and fractions

  1. 1. Solve, or say no solution / infinitely many:
    3(x+2)=3x+63(x + 2) = 3x + 6
  2. 2. Solve, or say no solution / infinitely many:
    2(y+1)=2y+52(y + 1) = 2y + 5
  3. 3. Solve:
    12n+4=14n+6\tfrac{1}{2}n + 4 = \tfrac{1}{4}n + 6
  4. 4. Solve:
    0.3m+2=0.1m+30.3m + 2 = 0.1m + 3
  5. 5. Solve:
    k+32=k+73\dfrac{k + 3}{2} = \dfrac{k + 7}{3}
  6. 6. Solve:
    4(2p−1)−3p=2(p+4)4(2p - 1) - 3p = 2(p + 4)

Answer Key

Level 3

  1. 1. infinitely many\text{infinitely many}
  2. 2. no solution\text{no solution}
  3. 3. n=8n = 8
  4. 4. m=5m = 5
  5. 5. k=5k = 5
  6. 6. p=4p = 4

Grade 8 Algebra: Word Problems: Solving Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 1

One- and two-step stories

  1. 1. Write an equation and solve:
    Ana\text{Ana}buys\text{buys}4\text{4}apples\text{apples}for\text{for}6\text{6}dollars\text{dollars}in\text{in}total.\text{total.}What\text{What}is\text{is}the\text{the}cost\text{cost}cc\text{}of\text{of}one\text{one}apple?\text{apple?}
  2. 2. Write an equation and solve:
    A\text{A}number\text{number}nn\text{}plus\text{plus}12\text{12}equals\text{equals}30.\text{30.}Find\text{Find}n.n\text{.}
  3. 3. Write an equation and solve:
    Tom\text{Tom}has\text{has}3\text{3}times\text{times}as\text{as}many\text{many}coins\text{coins}as\text{as}Lia.\text{Lia.}Tom\text{Tom}has\text{has}27\text{27}coins.\text{coins.}How\text{How}many\text{many}coins\text{coins}cc\text{}does\text{does}Lia\text{Lia}have?\text{have?}
  4. 4. Write an equation and solve:
    After\text{After}spending\text{spending}8\text{8}dollars,\text{dollars,}Maya\text{Maya}has\text{has}15\text{15}dollars\text{dollars}left.\text{left.}How\text{How}much\text{much}money\text{money}mm\text{}did\text{did}she\text{she}start\text{start}with?\text{with?}
  5. 5. Write an equation and solve:
    A\text{A}pack\text{pack}of\text{of}5\text{5}pencils\text{pencils}costs\text{costs}4\text{4}dollars.\text{dollars.}What\text{What}is\text{is}the\text{the}price\text{price}pp\text{}of\text{of}one\text{one}pencil?\text{pencil?}
  6. 6. Write an equation and solve:
    Twice\text{Twice}a\text{a}number\text{number}x,x\text{,}plus\text{plus}7,\text{7,}is\text{is}25.\text{25.}Find\text{Find}x.x\text{.}

Answer Key

Level 1

  1. 1. 4c=6,  c=1.54c = 6,\; c = 1.5
  2. 2. n+12=30,  n=18n + 12 = 30,\; n = 18
  3. 3. 3c=27,  c=93c = 27,\; c = 9
  4. 4. m−8=15,  m=23m - 8 = 15,\; m = 23
  5. 5. 5p=4,  p=0.85p = 4,\; p = 0.8
  6. 6. 2x+7=25,  x=92x + 7 = 25,\; x = 9

Grade 8 Algebra: Word Problems: Solving Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Rates and fixed costs

  1. 1. Write an equation and solve:
    A\text{A}phone\text{phone}plan\text{plan}costs\text{costs}15\text{15}dollars\text{dollars}per\text{per}month\text{month}plus\text{plus}0.05\text{0.05}dollars\text{dollars}per\text{per}text.\text{text.}The\text{The}bill\text{bill}is\text{is}20\text{20}dollars.\text{dollars.}How\text{How}many\text{many}texts\text{texts}tt\text{}were\text{were}sent?\text{sent?}
  2. 2. Write an equation and solve:
    A\text{A}taxi\text{taxi}charges\text{charges}3\text{3}dollars\text{dollars}plus\text{plus}2\text{2}dollars\text{dollars}per\text{per}mile.\text{mile.}A\text{A}ride\text{ride}costs\text{costs}19\text{19}dollars.\text{dollars.}How\text{How}many\text{many}miles\text{miles}mm\text{}was\text{was}the\text{the}ride?\text{ride?}
  3. 3. Write an equation and solve:
    Movie\text{Movie}tickets\text{tickets}cost\text{cost}9\text{9}dollars\text{dollars}each\text{each}plus\text{plus}a\text{a}4\text{4}dollar\text{dollar}booking\text{booking}fee.\text{fee.}Ben\text{Ben}pays\text{pays}40\text{40}dollars.\text{dollars.}How\text{How}many\text{many}tickets\text{tickets}tt\text{}did\text{did}he\text{he}buy?\text{buy?}
  4. 4. Write an equation and solve:
    The\text{The}sum\text{sum}of\text{of}two\text{two}consecutive\text{consecutive}integers\text{integers}is\text{is}45.\text{45.}Find\text{Find}the\text{the}smaller\text{smaller}integer\text{integer}n.n\text{.}
  5. 5. Write an equation and solve:
    Kim\text{Kim}has\text{has}30\text{30}dollars\text{dollars}and\text{and}saves\text{saves}12\text{12}dollars\text{dollars}per\text{per}week.\text{week.}After\text{After}how\text{how}many\text{many}weeks\text{weeks}ww\text{}will\text{will}she\text{she}have\text{have}102\text{102}dollars?\text{dollars?}
  6. 6. Write an equation and solve:
    A\text{A}gym\text{gym}charges\text{charges}25\text{25}dollars\text{dollars}to\text{to}join\text{join}plus\text{plus}10\text{10}dollars\text{dollars}per\text{per}month.\text{month.}Jo\text{Jo}paid\text{paid}85\text{85}dollars.\text{dollars.}How\text{How}many\text{many}months\text{months}mm\text{}did\text{did}she\text{she}go?\text{go?}

Answer Key

Level 2

  1. 1. 15+0.05t=20,  t=10015 + 0.05t = 20,\; t = 100
  2. 2. 3+2m=19,  m=83 + 2m = 19,\; m = 8
  3. 3. 9t+4=40,  t=49t + 4 = 40,\; t = 4
  4. 4. n+(n+1)=45,  n=22n + (n + 1) = 45,\; n = 22
  5. 5. 30+12w=102,  w=630 + 12w = 102,\; w = 6
  6. 6. 25+10m=85,  m=625 + 10m = 85,\; m = 6

Grade 8 Algebra: Word Problems: Solving Equations

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Geometry, ages and comparisons

  1. 1. Write an equation and solve:
    A\text{A}garden\text{garden}is\text{is}3\text{3}meters\text{meters}longer\text{longer}than\text{than}it\text{it}is\text{is}wide.\text{wide.}Its\text{Its}perimeter\text{perimeter}is\text{is}34\text{34}meters.\text{meters.}Find\text{Find}the\text{the}width\text{width}w.w\text{.}
  2. 2. Write an equation and solve:
    Gym\text{Gym}A\text{A}costs\text{costs}30\text{30}dollars\text{dollars}plus\text{plus}5\text{5}dollars\text{dollars}per\text{per}visit.\text{visit.}Gym\text{Gym}BB\text{}costs\text{costs}8\text{8}dollars\text{dollars}per\text{per}visit.\text{visit.}After\text{After}how\text{how}many\text{many}visits\text{visits}vv\text{}do\text{do}they\text{they}cost\text{cost}the\text{the}same?\text{same?}
  3. 3. Write an equation and solve:
    Leo\text{Leo}is\text{is}4\text{4}years\text{years}older\text{older}than\text{than}Sara.\text{Sara.}Their\text{Their}ages\text{ages}add\text{add}up\text{up}to\text{to}30.\text{30.}How\text{How}old\text{old}is\text{is}Sara?\text{Sara?}Use\text{Use}ss\text{}for\text{for}her\text{her}age.\text{age.}
  4. 4. Write an equation and solve:
    The\text{The}sum\text{sum}of\text{of}three\text{three}consecutive\text{consecutive}integers\text{integers}is\text{is}72.\text{72.}Find\text{Find}the\text{the}smallest\text{smallest}integer\text{integer}n.n\text{.}
  5. 5. Write an equation and solve:
    A\text{A}shirt\text{shirt}costs\text{costs}20\text{20}dollars\text{dollars}on\text{on}sale.\text{sale.}That\text{That}is\text{is}5\text{5}dollars\text{dollars}less\text{less}than\text{than}half\text{half}the\text{the}original\text{original}price\text{price}p.p\text{.}Find\text{Find}p.p\text{.}
  6. 6. Write an equation and solve:
    Plan\text{Plan}A\text{A}costs\text{costs}40\text{40}dollars\text{dollars}plus\text{plus}2\text{2}dollars\text{dollars}per\text{per}GB.\text{GB.}Plan\text{Plan}BB\text{}costs\text{costs}25\text{25}dollars\text{dollars}plus\text{plus}5\text{5}dollars\text{dollars}per\text{per}GB.\text{GB.}For\text{For}how\text{how}many\text{many}GB\text{GB}gg\text{}do\text{do}they\text{they}cost\text{cost}the\text{the}same?\text{same?}

Answer Key

Level 3

  1. 1. 2(w+3)+2w=34,  w=72(w + 3) + 2w = 34,\; w = 7
  2. 2. 30+5v=8v,  v=1030 + 5v = 8v,\; v = 10
  3. 3. s+(s+4)=30,  s=13s + (s + 4) = 30,\; s = 13
  4. 4. 3n+3=72,  n=233n + 3 = 72,\; n = 23
  5. 5. 12p−5=20,  p=50\tfrac{1}{2}p - 5 = 20,\; p = 50
  6. 6. 40+2g=25+5g,  g=540 + 2g = 25 + 5g,\; g = 5