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Section 3.4 Solving Equations with Distribution on Both Sides

Learn to solve equations using the distributive property on both sides. Distribute first, simplify, and move the variable to the positive side using inverse relationships. Practice with examples and find solutions to equations.

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Section 3.4 Solving Equations with Distribution on Both Sides

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  1. Section 3.4Solving Equations with Distribution on Both Sides Goal: Solve equations that use the distributive property on both sides.

  2. Basics Distribute First! Simplify the expression (combine like terms) Goal: Move the variable to the positive side Solve the Equation using Inverse Relationships Remember: You always want to solve for the Variable, “X = ?”

  3. Solve. 2x + 4 = 5x - 17 2x + 4 = 5x - 17 2x + 4 = 5x - 17 -2x -2x -5x -5x 4 = 3x - 17 -3x + 4 =-17 +17 +17 -4 -4 21 = 3x -3x = -21 3 3 -3 - 3 7 = x x = 7

  4. Identify Number of Solutions 4 (1- x ) + 3x = -2(x + 1) 4 - 4x + 3x = -2x - 2 4 – x = - 2x - 2 +2x + 2x 4 + 1x = -2 -4 -4 x = -6

  5. Solve. 4(x - 2) - 2x = 5(x - 3) 4x - 8 - 2x = 5x - 15 2x - 8 = 5x - 15 -2x -2x -8 = 3x - 15 +15 +15 7 = 3x 3 3

  6. Use a variable equation to solve. Find a number that is 20 more than 4 times its opposite. Let x = the number -x = the opposite x = 4(-x) + 20 x = -4x + 20 +4x +4x 5x = 20 5 5 x = 4

  7. Practice • p + 2p -3 = 6 + 4p • -2y = 3y – 18 -5y • 3 + 4(x + 5) = 31 – 10x • Show All work • USE YOUR NOTES

  8. Homework • Worksheet • Show all WORK • Due on Friday, October 11! • Extra 5 points if you turn in completed on Thursday, October 10!

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