2.2 Solving Equations with Variables on Both Sides

Review: Solve 4 = 7x - 3x 4 = 4x 4 4 1 = x 4 = 7(1) - 3(1) 4 4 1 = x 4 = 7(1) - 3(1) Draw “the river” – Notice the variables are on the same side! Combine like terms Divide both sides by 4 Simplify Check your answer

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.

1) Solve 3x + 2 = 4x - 1 - 3x - 3x 2 = x - 1 + 1 + 1 3 = x + 1 + 1 3 = x 3(3) + 2 = 4(3) - 1 9 + 2 = 12 - 1 Draw “the river” Subtract 3x from both sides Simplify Add 1 to both sides Check your answer

2) Solve 8y - 9 = -3y + 2 + 3y + 3y 11y – 9 = 2 + 9 + 9 11y = 11 11 11 + 9 + 9 11y = 11 11 11 y = 1 8(1) - 9 = -3(1) + 2 Draw “the river” Add 3y to both sides Simplify Add 9 to both sides Divide both sides by 11 Check your answer

What is the value of x if 3 - 4x = 18 + x? -3 3

3) Solve 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6 Draw “the river” Clear the fraction – multiply each term by the LCD Simplify Add 2x to both sides Add 6 to both sides Divide both sides by 6 Check your answer 3 - 2x = 4x – 6 + 2x +2x 3 = 6x – 6 + 6 + 6 9 = 6x 6 6 or 1.5 = x