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8th grade · Math · Unit 11 of 19

Equations with Brackets

Solve ax = b, x ÷ a = b, ax + b = c and a(x + b) = c

What your child practices

Solving one-variable equations, including ones with brackets and negative numbers, checking by substitution, and spotting a common mistake with the distributive property.

New York State Learning Standards learning standard: NY-8.EE.7 · solving linear equations that need the distributive property

How we explain it

Children can open this short lesson before they practice.

  1. Undo brackets by dividing both sides, or by expanding.
  2. Do the same thing to both sides.
  3. Check by putting your answer back into the equation.

Example: Solve 2(x + 3) = 14. Divide both sides by 2: x + 3 = 7. Subtract 3: x = 4. Answer: x = 4

Equations with Brackets in New York

In the New York State Learning Standards, this is unit 11 of 19 in 8th grade Math, after Tables, Graphs & Linear Relations and before Congruent Shapes.

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: New York State Education Department (NYSED)

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

    Dev wrote 4(x + 7) = 28 as 4x + 7 = 28. What went wrong?

    • He should have divided by x first.
    • He multiplied only x by 4. The 7 must be multiplied by 4 too.
    • Nothing. The two equations are equivalent.
    • He should have subtracted 4 from both sides.

  2. Question 2

    Which value of x makes 6x + 4 = 10 true?

    • 2
    • 1
    • 3
    • 0

  3. Question 3

    Solve for x: 7x − 6 = -48

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  4. Question 4

    Solve for x: x ÷ 6 = -2

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  5. Question 5

    Solve for x: 5(x − 3) = -55

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  6. Question 6

    Solve for x: 6x = 24

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