9th grade · Math · Unit 3 of 17
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.
Minnesota K-12 Academic Standards benchmark: 9.3.5.7 · using the structure of an equation to solve it
How we explain it
Children can open this short lesson before they practice.
- Expand brackets first.
- Collect like terms.
- 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 Minnesota
In the Minnesota K-12 Academic Standards, this is unit 3 of 17 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.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Solve for x: 6(x + 2) = −60
answer box
-12
Hint: Divide both sides by 6: x + 2 = −10. Subtract 2: x = −12.
Question 2
Solve for x: 6x + 4 = 5x + 8
answer box
4
Hint: Collect the x terms: 6x − 5x = 8 − 4, so 1x = 4. Divide by 1: x = 4.
Question 3
Solve for x: 3(x + 4) = (x − 2) + 16
answer box
1
Hint: Expand: 3x + 12 = 1x − 2 + 16. Collect: 2x = 2. Divide by 2: x = 1.
Question 4
Solve for x: x/4 + 5 = 8
answer box
12
Hint: Subtract 5: x/4 = 3. Multiply both sides by 4: x = 12.
Question 5
Solve for x: x/2 + x/3 = 25
answer box
30
Hint: Use a common denominator of 6: 3x/6 + 2x/6 = 25, so 5x = 150. Then x = 30.
Question 6
Kofi's gym charges $38 to join plus $8 per visit. Another gym charges $78 to join plus $3 per visit. After how many visits do the two gyms cost the same?
answer box
8
Hint: Set the costs equal: 38 + 8n = 78 + 3n. Then 5n = 40, so n = 8.