Algebra 1: Concepts and Skills

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Chapter 3 : Solving Linear Equations
3.6 Solving Decimal Equations

#### 3.6 Problem Solving Help

Help for Exercises 39-42 on page 167

The equations in Exercises 39-42 include decimals. You many find it easier to solve an equation with integers instead of decimals. One way to solve an equation that includes decimals is to first multiply each side of the equation by the same power of ten to get an equivalent equation that has integer coefficients instead of decimal coefficients.

When you do this, be sure to multiply each side of the equation by the power of ten that will eliminate all decimals. For example, multiply by 100 if there are decimals in the hundredths place, multiply by 1000 if there are decimals in the thousandths place, and so on. And be sure that you multiply each side of the equation by the same power of ten, or you will not get an equation that is equivalent to the original.

If you are comfortable using decimals, you can solve equations which include decimals without multiplying each side of the equation by a power of ten to eliminate decimal coefficients. Refer to the example on page 167 of your textbook which immediately precedes Exercises 39-42. The equation solved in this example, 4.5 - 7.2x = 3.4x - 49.5, can also be solved as shown below.

Notice that both methods give the same solution.