Linear Equations practice questions

Linear Equations questions

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1. 1Linear equationsFoundation

   If 3x + 5 = 23, what is the value of x?If 3x + 5 = 23, what is the value of x?

   • A66
   • B44
   • C2828
   • D88
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   Answer: 66

   Subtract 5 from both sides to get 3x = 18. Divide by 3, so x = 6.Subtract 5 from both sides to get 3x = 18. Divide by 3, so x = 6.

   How did you do?Got itMissed it
2. 2Linear equationsFoundation

   What is the value of x in x + 34 = 5?What is the value of x in (x + 3)/4 = 5?

   • A77
   • B1717
   • C2020
   • D2323
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   Answer: 1717

   Multiply both sides by 4: x + 3 = 20. Subtract 3 to get x = 17.Multiply both sides by 4: x + 3 = 20. Subtract 3 to get x = 17.

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3. 3Linear equationsFoundation

   What is the solution to 4 - 2x = 10?What is the solution to 4 - 2x = 10?

   • A33
   • B-3-3
   • C22
   • D-2-2
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   Answer: -3-3

   Subtract 4 from both sides: -2x = 6. Divide by -2, so x = -3.Subtract 4 from both sides: -2x = 6. Divide by -2, so x = -3.

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4. 4Linear equationsFoundation

   What is the solution to 2(3x - 1) = 4x + 8?What is the solution to 2(3x - 1) = 4x + 8?

   • A55
   • B33
   • C44
   • D66
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   Answer: 55

   Distribute to get 6x - 2 = 4x + 8. Subtract 4x and add 2 to get 2x = 10, so x = 5.Distribute to get 6x - 2 = 4x + 8. Subtract 4x and add 2 to get 2x = 10, so x = 5.

   How did you do?Got itMissed it
5. 5Linear equationsFoundation

   What is the solution to 7 - 3(x - 1) = 1?What is the solution to 7 - 3(x - 1) = 1?

   • A33
   • B22
   • C11
   • D-3-3
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   Answer: 33

   Distribute carefully: 7 - 3x + 3 = 1, so 10 - 3x = 1. Then -3x = -9 and x = 3. Writing 7 - 3x - 3 is the common slip.Distribute carefully: 7 - 3x + 3 = 1, so 10 - 3x = 1. Then -3x = -9 and x = 3. Writing 7 - 3x - 3 is the common slip.

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6. 6Linear equationsFoundation

   If 8 - 2x = 3x - 7, what is the value of x?If 8 - 2x = 3x - 7, what is the value of x?

   • A-3-3
   • B1515
   • C33
   • D11
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   Answer: 33

   Collect the variable on the side that keeps it positive: adding 2x gives 8 = 5x - 7, then adding 7 gives 15 = 5x, so x = 3. Choosing that side first avoids a sign error later.Collect the variable on the side that keeps it positive: adding 2x gives 8 = 5x - 7, then adding 7 gives 15 = 5x, so x = 3. Choosing that side first avoids a sign error later.

   How did you do?Got itMissed it
7. 7Linear equationsFoundation

   What is the y-intercept of the line 3x - 5y = 20?What is the y-intercept of the line 3x - 5y = 20?

   • A-4-4
   • B44
   • C2020
   • D-20-20
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   Answer: -4-4

   Set x = 0: -5y = 20, so y = -4. Rearranging into y = (35)x - 4 shows the same thing. Reading 20 off the equation forgets that it has not yet been divided by the coefficient of y.Set x = 0: -5y = 20, so y = -4. Rearranging into y = (3/5)x - 4 shows the same thing. Reading 20 off the equation forgets that it has not yet been divided by the coefficient of y.

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8. 8Linear equationsFoundation

   What is the solution to 3(x + 2) = 4x - 5?What is the solution to 3(x + 2) = 4x - 5?

   • A11
   • B1111
   • C-11-11
   • D33
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   Answer: 1111

   Expanding gives 3x + 6 = 4x - 5. Subtracting 3x leaves 6 = x - 5, so x = 11. Check: 3(13) = 39 and 4(11) - 5 = 39.Expanding gives 3x + 6 = 4x - 5. Subtracting 3x leaves 6 = x - 5, so x = 11. Check: 3(13) = 39 and 4(11) - 5 = 39.

   How did you do?Got itMissed it
9. 9Linear equationsFoundation

   If 2x/3 = 8, what is the value of x?If 2x/3 = 8, what is the value of x?

   • A1616
   • B5.335.33
   • C2424
   • D1212
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   Answer: 1212

   Multiplying both sides by 3 gives 2x = 24, so x = 12. Multiplying by 3 without then halving gives 24, which is the step most often left out.Multiplying both sides by 3 gives 2x = 24, so x = 12. Multiplying by 3 without then halving gives 24, which is the step most often left out.

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10. 10Linear equationsFoundation

    What is the solution to 7 - 2x = x + 1?What is the solution to 7 - 2x = x + 1?

    • A-2-2
    • B838/3
    • C66
    • D22
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    Answer: 22

    Add 2x to both sides: 7 = 3x + 1. Subtract 1: 6 = 3x, so x = 2. Check: 7 - 4 = 3 and 2 + 1 = 3.Add 2x to both sides: 7 = 3x + 1. Subtract 1: 6 = 3x, so x = 2. Check: 7 - 4 = 3 and 2 + 1 = 3.

    How did you do?Got itMissed it
11. 11Linear equationsStandard

    What is the solution to 5(x - 2) = 3x + 10?What is the solution to 5(x - 2) = 3x + 10?

    • A55
    • B1515
    • C2020
    • D1010
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    Answer: 1010

    Expand first: 5x - 10 = 3x + 10. Subtract 3x and add 10: 2x = 20, so x = 10.Expand first: 5x - 10 = 3x + 10. Subtract 3x and add 10: 2x = 20, so x = 10.

    How did you do?Got itMissed it
12. 12Linear equationsStandard

    What is the solution to 2x3 - 1 = 5?What is the solution to (2x)/3 - 1 = 5?

    • A99
    • B1212
    • C88
    • D66
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    Answer: 99

    Add 1 to both sides to get 2x / 3 = 6. Multiply by 3 to get 2x = 18, so x = 9.Add 1 to both sides to get 2x / 3 = 6. Multiply by 3 to get 2x = 18, so x = 9.

    How did you do?Got itMissed it
13. 13Linear equationsStandard

    If 3x - 12 = x + 73, what is the value of x?If (3x - 1)/2 = (x + 7)/3, what is the value of x?

    • A55
    • B17717/7
    • C171117/11
    • D33
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    Answer: 17717/7

    Cross-multiply: 3(3x - 1) = 2(x + 7), so 9x - 3 = 2x + 14. Then 7x = 17 and x = 177.Cross-multiply: 3(3x - 1) = 2(x + 7), so 9x - 3 = 2x + 14. Then 7x = 17 and x = 17/7.

    How did you do?Got itMissed it
14. 14Linear equationsStandard

    If 4(x + 2) - 3 = 2(x + 9), what is the value of x?If 4(x + 2) - 3 = 2(x + 9), what is the value of x?

    • A55
    • B88
    • C6.56.5
    • D3.53.5
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    Answer: 6.56.5

    Distribute both sides: 4x + 8 - 3 = 2x + 18, so 4x + 5 = 2x + 18. Then 2x = 13 and x = 6.5.Distribute both sides: 4x + 8 - 3 = 2x + 18, so 4x + 5 = 2x + 18. Then 2x = 13 and x = 6.5.

    How did you do?Got itMissed it
15. 15Linear equationsStandard

    What is the solution to 2(x - 4) = 3x + 1?What is the solution to 2(x - 4) = 3x + 1?

    • A-7-7
    • B-9-9
    • C99
    • D77
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    Answer: -9-9

    Expanding gives 2x - 8 = 3x + 1. Subtracting 2x from both sides leaves -8 = x + 1, so x = -9. Check it: 2(-13) = -26 and 3(-9) + 1 = -26.Expanding gives 2x - 8 = 3x + 1. Subtracting 2x from both sides leaves -8 = x + 1, so x = -9. Check it: 2(-13) = -26 and 3(-9) + 1 = -26.

    How did you do?Got itMissed it
16. 16Linear equationsStandard

    What is the x-intercept of the line 5x - 2y = 20?What is the x-intercept of the line 5x - 2y = 20?

    • A44
    • B-10-10
    • C1010
    • D-4-4
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    Answer: 44

    The x-intercept is where y = 0, so 5x = 20 and x = 4. Setting x to zero instead gives the y-intercept, -10, which is the commonest confusion here.The x-intercept is where y = 0, so 5x = 20 and x = 4. Setting x to zero instead gives the y-intercept, -10, which is the commonest confusion here.

    How did you do?Got itMissed it
17. 17Linear equationsStandard

    What is the y-intercept of the line 3x + 2y = 12?What is the y-intercept of the line 3x + 2y = 12?

    • A44
    • B1212
    • C66
    • D-6-6
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    Answer: 66

    The y-intercept is where x = 0, so 2y = 12 and y = 6. Setting y to zero instead gives the x-intercept of 4, which is the usual confusion.The y-intercept is where x = 0, so 2y = 12 and y = 6. Setting y to zero instead gives the x-intercept of 4, which is the usual confusion.

    How did you do?Got itMissed it
18. 18Linear equationsStandard

    Enter the solution to 5(x - 2) = 3x + 4.Enter the solution to 5(x - 2) = 3x + 4.

    Student-produced response: write your own answer rather than choosing one.

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    Answer: 77

    Expanding gives 5x - 10 = 3x + 4. Subtracting 3x leaves 2x - 10 = 4, so 2x = 14 and x = 7.Expanding gives 5x - 10 = 3x + 4. Subtracting 3x leaves 2x - 10 = 4, so 2x = 14 and x = 7.

    How did you do?Got itMissed it