2.1.3 Solving Two-Step Equations Key Objectives

• Solve two-step equations. • Write two-step equations. • Solve equations that contain fractions.

In a two-step equation, two operations (typically multiplication or division and addition or subtraction) are preformed on the variable. The following equations are examples of two-step equations. 5 x + 3 = 13

= − x

1

2

3

Two-step equations can be solved in two steps using inverse operations, as demonstrated in the examples below. Remember to always apply operations to both sides of an equation when solving. Example 1 Solving Two-Step Equations By the order of operations, the variable in the equation 9 x − 2 = 25 is multiplied by 9 first and then 2 is subtracted from that product. To solve the equation, undo these operations in the reverse of the order of operations. So, undo the subtraction first and then undo the multiplication.

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