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Exercises Numbers, fractions and percents

Example 4.102 from Prealgebra, 4.7 Solve Equations with Fractions

Solve Equations with Fractions: example 4.102

Solve: $\frac{3}{4} x = 24 .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Multiply both sides by the reciprocal of the coefficient.

Simplify.

Multiply.

Check:

Substitute $x = 32$ .

Rewrite $32$ as a fraction.

Multiply. The equation is true.

Notice that in the equation $\frac{3}{4} x = 24,$ we could have divided both sides by $\frac{3}{4}$ to get $x$ by itself. Dividing is the same as multiplying by the reciprocal, so we would get the same result. But most people agree that multiplying by the reciprocal is easier.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve: $\frac{2}{5} n = 14 .$

How did it go?

PreviousSolve Equations with Fractions: example 4.101 Next Solve Equations with Fractions: example 4.103

From Prealgebra (1st edition) by OpenStax (Rice University), section 4.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.