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Exercises Equations and inequalities

Example 8.16 from Prealgebra, 8.2 Solve Equations Using the Division and Multiplication Properties of Equality

Solve Equations Using the Division and Multiplication Properties of Equality: example 8.16

Solve: $\frac{2}{3} x = 18 .$

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
Since the product of a number and its reciprocal is $1,$ our strategy will be to isolate $x$ by multiplying by the reciprocal of $\frac{2}{3} .$

Multiply by the reciprocal of $\frac{2}{3}$ .

Reciprocals multiply to one.

Multiply.

Check your answer. Let $x = 27$

Notice that we could have divided both sides of the equation $\frac{2}{3} x = 18$ by $\frac{2}{3}$ to isolate $x .$ While this would work, multiplying by the reciprocal requires fewer steps.

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 Using the Division and Multiplication Properties of Equality: example 8.15 Next Solve Equations Using the Division and Multiplication Properties of Equality: example 8.17

From Prealgebra (1st edition) by OpenStax (Rice University), section 8.2, 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.