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Solving Equations

Solving Equations. Steps:. 1. If there are fractions, multiply by the LCD 2. Distribute if necessary 3. Combine like terms on the same side 4. Get variables on the same side 5. Get constants on the opposite side of the variable 6. Divide by the coefficient. 1) Solve. 3x + 2 = 4x - 1.

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Solving Equations

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  1. Solving Equations

  2. Steps: • 1. If there are fractions, multiply by the LCD • 2. Distribute if necessary • 3. Combine like terms on the same side • 4. Get variables on the same side • 5. Get constants on the opposite side of the variable • 6. Divide by the coefficient

  3. 1) Solve. 3x + 2 = 4x - 1 You need to get the variables on one side of the equation. It does not matter which variable you move. Try to move the one that will keep your variable positive.

  4. 1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x 3(3) + 2 = 4(3) - 1 9 + 2 = 12 - 1 • Subtract 3x from both sides • Simplify • Add 1 to both sides • Simplify • Check your answer

  5. 2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11 y = 1 8(1) - 9 = -3(1) + 2 • Add 3y to both sides • Simplify • Add 9 to both sides • Simplify • Divide both sides by 11 • Simplify • Check your answer

  6. Answer Now What is the value of x if 3 - 4x = 18 + x? • -3 • 3

  7. 3) Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) • Combine like terms • Divide both sides by 4 • Simplify • Check your answer

  8. -7x + 21 = -7 - 21 - 21 -7x = -28 -7 -7 x = 4 -7(4 - 3) = -7 -7(1) = -7 • Distribute • Subtract 21 from both sides • Simplify • Divide both sides by -7 • Simplify • Check your answer 4) Solve -7(x - 3) = -7

  9. Answer Now What is the value of x if 3(x + 4) = 2(x - 1)? • -14 • -13 • 13 • 14

  10. 5) Solve • Clear the fraction – multiply each term by the LCD • Simplify • Add 2x to both sides • Simplify • Add 6 to both sides • Simplify • Divide both sides by 6 • Simplify • Check your answer 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6 or 1.5 = x

  11. Special Case #1 6) 2x + 5 = 2x - 3 -2x -2x 5 = -3 This is never true! No solutions • Subtract 2x from both sides • Simplify

  12. Special Case #2 7) 3(x + 1) - 5 = 3x - 2 3x + 3 – 5 = 3x - 2 3x - 2 = 3x – 2 -3x -3x -2 = -2 This is always true! Infinite solutions or identity • Distribute • Combine like terms • Subtract 3x from both sides • Simplify

  13. Answer Now What is the value of x if -3 + 12x = 12x - 3? • 0 • 4 • No solutions • Infinite solutions

  14. Answer Now Challenge! What is the value of x if -8(x + 1) + 3(x - 2) = -3x + 2? • -8 • -2 • 2 • 8

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