Section 1-3: Solving Equations

To solve equations you want to get the variable on one side, and all of the other numbers on the other side. To do this you use the order of operations “backwards”.

Let’s put the variables on the LEFT side. 2(x – 4) = 3x – 7 Distribute and gather like terms on each side. 2x – 8 = 3x – 7 Let’s put the variables on the LEFT side. -3x = -3x -x – 8 = -7 Add 8 to both sides. + 8 = + 8 -x = 1 Divide both sides by -1 X = -1

If you put the -1 in for the “x”, your equation should be true: 2(x – 4) = 3x – 7 2(-1 – 4) = 3(-1) – 7 2(-5) = -3 – 7 -10 = -10

You try: 5x + 17 – 2x = 2(6 – x)

Solving equations with all variables “LITERAL EQUATIONS” Solve for “b” a + b = d c If it helps, substitute numbers in for the OTHER variables so you can see what to do first. 1 + b = 4 a + b = d 3 c Multiply both sides by 3 (c) to get rid of fractions. 1 + b = 12  a + b = cd Subtract 1 (a) from both sides. b = 11 b = cd - a

You try: Solve ax – b = cd for “x”