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Equations and inequalities · Ages 12–13

Linear equations in one unknown worksheet

Covers: Equations and the balance, Unknowns on both sides, Equations with brackets, Fractions and decimals in equations, From words to an equation, Word problems with equations

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Linear equations in one unknown worksheet

Equations and inequalities · Ages 12–13

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

Part A: Working out and filling in (2 marks each)

  1. 1.8x + 21 = −19: take 21 from both sides, 8x = ; divide both by 8, x = .

    Fill in each blank

    Answer:

  2. 2.59 − 3x = 4x − 4, x =

    Answer:

  3. 3.−5 − 6(x − 7) = 13, x =

    Answer:

  4. 4.3(x − 7) = 5(x − 1), x =

    Answer:

  5. 5.58 x = 11, x =

    Answer in simplest form

    Answer:

  6. 6.x2 + x5 = −28, x =

    Answer:

  7. 7.May has 4 times as much money as Ka-lok. May spends $7 and Ka-lok is given $8, and then they have the same. With $x as Ka-lok's at first: May now has $(x − 7), Ka-lok has $(x + ), and solving gives x = .

    Fill in each blank

    Answer:

  8. 8.Ming buys 4 identical notebooks for $36 in all. With $x for one, the equation is 4x = 36, so x = .

    Answer:

  9. 9.17 coins, $5 and $2, $73 in all. 5x + 2(17 − x) = 73, 3x + = 73, x = .

    Fill in each blank

    Answer:

Part B: Choose, or true or false (2 marks each)

  1. 10.🧊 is 1 g and 🍎 is x g. What is x?

    • A. x = 6
    • B. x = 5
    • C. x = 3
    • D. x = 7

    Choose the right answer

    Answer:

  2. 11.Moving terms in 9x + 11 = 3x + 18 gives 9x − 3x = 7.

    True or false?

    Answer:

  3. 12."4 less than 3 times x is 10": which equation is it?

    • A. 3(x − 4) = 10
    • B. 3x − 4 = 10
    • C. 4 − 3x = 10
    • D. 3x + 4 = 10

    Choose the right answer

    Answer:

Part C: Word problems (4 marks each)

  1. 13.It is 26°C on the peak and falling 5°C an hour. After how many hours will it be −9°C?

    Working:

    Answer:

  2. 14.A: $65 fee, $32 a book. B: $37 a book. 37x = 32x + 65, x = 65, x = .

    Fill in each blank

    Working:

    Answer:

  3. 15.Put the steps of solving 5(x − 2) = 3(x + 4) in order.

    • A. 5(x − 2) = 3(x + 4)
    • B. 5x − 10 = 3x + 12
    • C. x = 11
    • D. 2x = 22

    Write the letters in the right order

    Working:

    Answer:

  4. 16.Spent 17 of the money, $24 left. x − x7 = 24. Times 7: 7x − x = , x = .

    Fill in each blank

    Working:

    Answer:

  5. 17.A rectangle's length is 9 cm more than 4 times its width, and its perimeter is 48 cm. With width x, which equation is right?

    • A. 2(4x + 9) = 48
    • B. 4x + 9 + x = 48
    • C. 2(4x + 9 + x) = 48
    • D. 2(4x + x) + 9 = 48

    Choose the right answer

    Working:

    Answer:

  6. 18.A, B and C have 126. A has 3 times B's, and C 6 more than B. How many has C?

    Working:

    Answer:

Show the answers and working

Linear equations in one unknown worksheet: Answers and working

Part A: Working out and filling in

  1. 1. −40, −5

    −19 − 21 = −40, −40 ÷ 8 = −5. Check with x = −5: 8x + 21 = −40 + 21 = −19.

  2. 2. 9

    Move the x terms right and the numbers left: 59 + 4 = 4x + 3x, so 7x = 59 + 4, x = 9.

  3. 3. 4

    A minus in front of the bracket: −5 − 6x + 42 = 13. So 6x = −5 + 42 − 13, x = 4.

  4. 4. −8

    Open up: 3x − 21 = 5x − 5. Move terms: −21 + 5 = 5x − 3x, so 2x = −16, x = −8.

  5. 5. 885

    Multiply both sides by the reciprocal, 85: x = 11 × 85 = 885. Or times 8 first, 5x = 88, then divide by 5.

  6. 6. −40

    Times 10: 5x + 2x = −280, 7x = −280, x = −40.

  7. 7. 4, 8, 5

    May had 4x, and after spending 7 has 4x − 7; Ka-lok with 8 more has x + 8. The same: 4x − 7 = x + 8, so x = 5.

  8. 8. 9

    4x = 36; divide both sides by 4: x = 36 ÷ 4 = 9. Check: 4 notebooks at $9 make $36.

  9. 9. 34, 13

    2 × 17 = 34; 3x = 73 − 34 = 39, x = 13. Supposing all were $2 gives the same: $39 short, $3 a swap.

Part B: Choose, or true or false

  1. 10. C. x = 3

    2x + 4 = 10. Take 4 🧊 off each side: 2x = 6, so x = 3.

  2. 11. True

    11 becomes −11 as it crosses, so the right side is 18 − 11.

  3. 12. B. 3x − 4 = 10

    3 times x is 3x, and 4 less than that is 3x − 4.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

  1. 13. 7 hours

    26 − 5x = −9, 5x = 26 + 9 = 35, x = 7. From 26 down to −9 is 26 + 9 degrees, not a difference.

  2. 14. 5, 13

    Each book saves $5, so 13 books make up the $65 membership.

  3. 15. A → B → D → C

    Open the brackets, move and collect the terms, then divide by 2.

  4. 16. 168, 28

    7 × 24 = 168, 6x = 168, x = 28. It isn't simply 24 × 7: what is left isn't 17.

  5. 17. C. 2(4x + 9 + x) = 48

    Length = 4x + 9, width = x; perimeter = 2 × (length + width).

  6. 18. 30 sweets

    Choosing B as x is easiest: 3x + x + (x + 6) = 126, 5x + 6 = 126, x = 24. C has 30.

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