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Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides. Steps to Solving:. Step 1: Eliminate Parentheses- Use distributive property 3(2x+3)= 7x - 3 + x Step 2: Combine all like terms 6x + 9 = 8x - 3 + x Step 3: Move all variables to one side of the equation 6x + 9 = 9x -3

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Solving Equations with Variables on Both Sides

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  1. Solving Equations with Variables on Both Sides

  2. Steps to Solving: • Step 1: Eliminate Parentheses- Use distributive property • 3(2x+3)= 7x - 3 + x • Step 2: Combine all like terms • 6x + 9 = 8x - 3 + x • Step 3: Move all variables to one side of the equation • 6x + 9 = 9x -3 • Step 4: Solve using inverse operations • 12 = 3x

  3. Example:3x – 8 = 5x + 2 • Follow steps: • Check your solution by substituting the value back into the original equation.

  4. Example:6p + p + 4 = 8p + 3 • Follow steps: • Check your solution by substituting the value back into the original equation.

  5. Solve.10z– 15 – 4z = 8 + 6z- 15 If variables cancel there is no solution!

  6. Solve.

  7. 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 florist’s bouquets cost the same price.

  8. Marla’s Gift Baskets sell a muffin basket for $22.00 plus $2.25 for every balloon. A competing service sells a similar muffin basket for $16.00 plus $3.00 for every balloon. Find the number of balloons that would make both gift basket companies muffin baskets cost the same price.

  9. Practice Solve. 1. 4x + 16 = 2x 2. 8x – 3 = 15 + 5x 3. 2(3x + 11) = 6x + 4 4.x = x – 9 5. An apple has about 30 calories more than an orange. Five oranges have about as many calories as 3 apples. How many calories are in each? x = –8 x = 6 no solution x = 36 An orange has 45 calories. An apple has 75 calories.

  10. Let’s Summarize! • What are the steps to solving with a variable on both sides? • Can a problem have no solution? When?

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