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Multi-Step Equations Worksheet

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Multi-Step Equations Worksheet

Solve each equation using clear, inverse-operation steps. Check solutions by substituting them into the original equation. For word problems, define your variable and include units where appropriate.

Stage 1 · Undo the operations

Start with brackets or other operations as needed. Show each step in your working.

1.An arcade game triples a player's points, then adds 7 bonus points. The final score is 34. Solve 3(x + 2) + 1 = 34 to find the starting score x.

2.Solve 5(2x - 3) - 4 = 31. Write at least three equations showing how you isolate x.

3.Kai solves 4(x - 2) + 3 = 19 like this: 4x - 8 + 3 = 19; 4x - 5 = 19; 4x = 14; x = 3.5. Is Kai correct? Identify the first incorrect line, then give the correct solution.

Stage 2 · Variables on both sides

Collect variable terms on one side and constants on the other. Keep the equation balanced at every step.

4.Solve 7x - 8 = 3x + 20. Show how you collect the x-terms and constants.

5.For 2(3x + 1) = 4x + 14, a student says the solution is x = 6. Decide whether this is true or false and verify by substitution.

TrueFalse

6.Match each equation to its solution. Use each solution once.

A. 3(x + 4) = 2x + 19
B. 5x - 6 = 2(x + 9)
C. 4(x - 1) + 2 = 3x + 7

2. x = 8
1. x = 7
3. x = 9

Stage 3 · Fractions and real situations

Translate each situation into an equation before solving. Check that your answer makes sense in context.

7.Solve (x - 2)/3 + 4 = 9. Show how you clear the fraction.

8.A food truck charges a $4 delivery fee plus $3 for each wrap. An order costs $25. Write and solve an equation to find the number of wraps ordered.

9.Xavier has $18 saved and puts away the same amount each week for 6 weeks. She then spends $12 and has $72 left. Let d be the amount saved each week. Form an equation and solve for d.

10.Create a multi-step equation with brackets that has x = 4 as its solution. Then show a substitution check proving your equation works.