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Solving Equations with Variables on Both Sides in Pre-Algebra

Learn how to solve multistep equations with variables on both sides by combining like terms, isolating the variable, and applying properties of equality. Follow step-by-step examples to master the concept.

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Solving Equations with Variables on Both Sides in Pre-Algebra

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  1. Solving Equations with Variables on Both Sides Pre-Algebra

  2. To solve multistep equations with variables on both sides: First combine like terms. Then add or subtract variable terms to both sides so that the variable occurs on only one side of the equation. Then use properties of equality to isolate the variable.

  3. –3x = –3 6 –3 Example 1: Solve. A. 4x + 6 = x 4x + 6 = x – 4x– 4x Subtract 4x from both sides. 6 = –3x Divide both sides by –3. –2 = x

  4. 4b 24 = 4 4 Example 2: Solve. B. 9b – 6 = 5b + 18 9b – 6 = 5b + 18 – 5b– 5b Subtract 5b from both sides. 4b – 6 = 18 + 6+ 6 Add 6 to both sides. 4b = 24 Divide both sides by 4. b = 6

  5. 9w + 3 = 7w + 7 Combine like terms. – 7w– 7w Subtract 7w from both sides. Example 3: Solve. C. 9w + 3 = 5w + 7 + 2w 9w + 3 = 5w + 7 + 2w 2w + 3 = 7 Subtract 3 from both sides. – 3– 3 Divide by 2 on both sides. 2w = 4 w = 2

  6. 8z8 = 8 8 Example 4: Solve. A. 10z – 15 – 4z = 8 – 2z - 15 10z – 15 – 4z = 8 – 2z – 15 6z– 15 = –2z– 7 Combine like terms. + 2z+ 2z Add 2z to both sides. 8z – 15 = – 7 + 15+15 Add 15 to both sides. 8z = 8 Divide both sides by 8. z = 1

  7. Xavier & Jonathon have the same number of super hero action figures in their collections. Xavier has 5 complete sets and 4 individual figures. Jonathon has 3 complete sets and 14 individual figures. How many figures make up a complete set? Let x equal the number of figures in a complete set. 5x + 4 = 3x + 14 Now solve…

  8. 2x = 2 10 2 5x + 4 = 3x + 14 Subtract 3x from both sides. – 3x– 3x 2x + 4 = 14 – 4– 4 Subtract 4 from both sides. 2x = 10 Divide both sides by 2. x = 5 Each complete set has 5 super hero action figures.

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