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# Solving Two-Step Equations Algebraically

Example 1

Solve the equation 12C + 10 = 46.

Solution

To solve this equation, the goal is to have C alone on one side of the equation. This means we must undo the addition by 10 and the multiplication by 12 that occur on the left side. We first eliminate the 10 on the left side by subtracting 10 from each side.

So the result of the first step is the equation 12C = 36. This equation can now be solved by dividing each side by 12.

 12C = 36 C = 3

So, te solution is x = 3.

Pay special attention to the steps that were used to solve the two-step equation in Example 1.

(1) Add to or subtract from each side to undo the subtraction or addition on one side of the equation. This will leave an equation involving only multiplication or division.

(2) Solve the resulting equation by dividing or multiplying each side of the equation to undo the multiplication or division.

Example 2

Solve -2x + 5 = 17.

Solution

Step 1 Subtract 5 from each side.

Step 2 Divide each side by - 2.

 -2x = 12 x = -6

Solve several equations by yourself. Practicing these algebra skills is very important. Be sure to solve some equations with negative coefficients, and some involving fractions.