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Equation Solving Techniques with Variables and Grouping Symbols

Learn how to solve equations with variables on both sides and grouping symbols step-by-step with examples and guided practice questions.

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Equation Solving Techniques with Variables and Grouping Symbols

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  1. ANSWER The solution is 2. Check by substituting 2 for xin the original equation. EXAMPLE 1 Solve an equation with variables on both sides Solve 7 – 8x= 4x– 17. 7 – 8x = 4x – 17 Write original equation. 7 – 8x + 8x = 4x – 17 + 8x Add 8xto each side. 7 = 12x – 17 Simplify each side. 24 = 12x Add 17 to each side. 2 = x Divide each side by 12.

  2. ? 7 – 8(2) = 4(2) – 17 ? –9 = 4(2) – 17 –9=–9 EXAMPLE 1 Solve an equation with variables on both sides CHECK 7 – 8x= 4x– 17 Write original equation. Substitute 2 for x. Simplify left side. Simplify right side. Solution checks.

  3. (16x + 60). Solve 9x–5= (16x + 60) 9x – 5= 1 1 4 4 EXAMPLE 2 Solve an equation with grouping symbols Write original equation. 9x – 5 = 4x + 15 Distributive property 5x – 5 = 15 Subtract 4xfrom each side. 5x =20 Add 5 to each side. x = 4 Divide each side by 5.

  4. ANSWER 3 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 1. 24 – 3m= 5m

  5. ANSWER 9 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 2. 20 +c= 4c – 7

  6. ANSWER –8 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 3. 9 – 3k= 17k – 2k

  7. ANSWER 6 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 4. 5z– 2= 2(3z – 4)

  8. ANSWER 2 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution. 5. 3 – 4a= 5(a – 3)

  9. 6. (6y + 15) 8y–6= ANSWER 4 2 3 for Examples 1 and 2 GUIDED PRACTICE Solve the equation. Check your solution.

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