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# Algebraic Equations Study Guide: GED Math (page 3)

By LearningExpress Editors
LearningExpress, LLC
Updated on Mar 23, 2011

### Solving Multiple-Step Algebraic Equations

The algebraic equations you've solved so far in this lesson have mostly required only one inverse operation. But some algebraic equations require more than one inverse operation to isolate the variable and then solve the equation.

When solving multiple-step algebraic equations, you should first add or subtract. Then, multiply or divide. In other words, you follow the order of operations in inverse order. Another way to look at it is to solve for the number attached to the variable last. Let's look at some examples.

Examples

1. Solve the following algebraic expression: 2m + 5 = 13.
2. First, look for numbers that are being added or subtracted to the term with the variable. In this equation, 5 is added to the 2m. To simplify, subtract 5 from both sides of the equation.

Perform the inverse operation for any multiplication or division. The variable in this equation is multiplied by 2, so you must divide each side of the equation by 2 in order to isolate the variable.

The answer is m = 4.

3. Solve the following algebraic equation: 5p + 24 = 3p – 4.
4. This equation has a variable on each side of the equal sign. So, you first need to get the variable terms on one side of the equation. You can do this by subtracting the smaller of the two variables from each side, because they have like terms.

Look for numbers that are being added to or subtracted from the term with the variable. In this equation, 24 is added to the 2p. So you subtract 24 from both sides of the equation.

Perform the inverse operation for any multiplication or division. The variable in this equation is multiplied by 2, so you divide each side of the equation by 2 to isolate the variable.

The answer is p = –14.

5. Solve the following algebraic equation: 4(b + 1) = 20.
6. This equation has parentheses, so you need to remove the parentheses by distributing the 4. 4(b + 1) = 4b + 4

So, your equation becomes 4b + 4 = 20.

Look for numbers that are being added to or subtracted from the term with the variable. Subtract 4 from both sides of the equation.

Perform the inverse operation for any multiplication or division. Divide each side of the equation by 4.

The answer is b = 4.

Practice problems for these concepts can be found at:

Algebra and Functions Practice Problems: GED Math

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