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Published byKerry Johnston Modified over 8 years ago

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**Learn to solve equations with variables on both sides of the equal sign.**

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

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

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Example 3: Solve. 9w + 3 = 9w + 7 9w + 3 = 9w + 7 – 9w – 9w Subtract 9w from both sides. 3 ≠ No solution. There is no number that can be substituted for the variable w to make the equation true.

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If the variables in an equation are eliminated and the resulting statement is false, the equation has no solution. Helpful Hint

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Practice- Example 5: Solve. 3b – 2 = 2b + 12 3b – 2 = 2b + 12 – 2b – 2b Subtract 2b from both sides. b – 2 = Add 2 to both sides. b =

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Practice- Example 6: Solve. 3w + 1 = 3w + 8 3w + 1 = 3w + 8 – 3w – 3w Subtract 3w from both sides. 1 ≠ No solution. There is no number that can be substituted for the variable w to make the equation true.

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

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Business Application Daisy’s Flowers sell a rose bouquet for $39.95 plus $2.95 for every rose. A competing florist sells a similar bouquet for $26.00 plus $4.50 for every rose. Find the number of roses that would make both florists’ bouquets cost the same price.

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