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8th grade · Math · Unit 14 of 15

Variables on Both Sides

Equations with x on both sides

What your child practices

Your child writes and solves equations with the variable on both sides of the equal sign, such as comparing two phone plans, and checks whether a value is a solution.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.8(A); 8.8(C) · writing and solving equations with variables on both sides

How we explain it

Children can open this short lesson before they practice.

  1. Get the variable on one side: subtract the smaller x term from both sides.
  2. Then undo adding or subtracting, and divide by the number in front of x.
  3. Check by putting the answer back into both sides.

Example: Solve 5x + 2 = 3x + 10. Subtract 3x from both sides: 2x + 2 = 10. Subtract 2: 2x = 8. Divide by 2: x = 4. Answer: x = 4

Variables on Both Sides in Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 14 of 15 in 8th grade Math, after Systems of Equations and before Loans, Interest & College.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Texas Education Agency (TEA)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Plan A costs $41 plus $7 a month. Plan B costs $5 plus $10 a month. After how many months do they cost the same?

    • 11
    • 13
    • 24
    • 12

  2. Question 2

    Plan A costs $30 plus $7 a month. Plan B costs $10 plus $9 a month. After how many months do they cost the same?

    • 11
    • 10
    • 20
    • 9

  3. Question 3

    Solve for x: 6x + 3 = 2x + 31

    • 8
    • −7
    • 28
    • 7

  4. Question 4

    Solve for x: 3x + 5 = x + 15

    • 10
    • −5
    • 5
    • 6

  5. Question 5

    Is x = 4 a solution of 8x = 5x + 12?

    • No
    • Yes

  6. Question 6

    Is x = 2 a solution of 2x − 6 = x − 4?

    • No
    • Yes

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