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9th grade · Math · Unit 3 of 22

Multi-Step Equations

Brackets, fractions and both sides

What your child practices

Solving linear equations with brackets, fractions and variables on both sides, checking solutions, and turning word problems into equations.

New York State Learning Standards learning standard: AI-A.REI.1; AI-A.REI.3 · solving multi-step linear equations and explaining each step

How we explain it

Children can open this short lesson before they practice.

  1. Expand brackets first.
  2. Collect like terms.
  3. Then undo adding or subtracting, and finally multiplying or dividing.

Example: 2(x + 3) = 14 Expand: 2x + 6 = 14. Subtract 6: 2x = 8. Divide by 2: x = 4. Answer: x = 4

Multi-Step Equations in New York

In the New York State Learning Standards, this is unit 3 of 22 in 9th grade Math, after Polynomials and before Linear Relations.

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

    Solve for x: 4(x + 7) = 52

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  2. Question 2

    Solve for x: 6x − 8 = 5x − 14

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  3. Question 3

    Solve for x: 8(x + 4) = 4(x − 1) + 0

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  4. Question 4

    Solve for x: x/4 + 2 = −2

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  5. Question 5

    Solve for x: x/4 + x/6 = 10

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  6. Question 6

    Leo's gym charges $20 to join plus $2 per visit. Another gym charges $27 to join plus $1 per visit. After how many visits do the two gyms cost the same?

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