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Exercises Numbers, fractions and percents

Example 3.60 from Prealgebra, 3.5 Solve Equations Using Integers; The Division Property of Equality

Solve Equations Using Integers; The Division Property of Equality: example 3.60

Determine whether each of the following is a solution of $2 x - 5 = −13 :$

ⓐ $x = 4$
ⓑ $x = −4$
ⓒ $x = −9 .$

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

ⓐ Substitute 4 for x in the equation to determine if it is true.

Multiply.

Subtract.

Since $x = 4$ does not result in a true equation, $4$ is not a solution to the equation.

ⓑ Substitute −4 for x in the equation to determine if it is true.

Multiply.

Subtract.

Since $x = −4$ results in a true equation, $−4$ is a solution to the equation.

ⓒ Substitute −9 for x in the equation to determine if it is true.

Substitute −9 for x.

Multiply.

Subtract.

Since $x = −9$ does not result in a true equation, $−9$ is not a solution to the equation.

Your turn

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

Determine whether each of the following is a solution of $2 x - 8 = −14 :$

ⓐ $x = −11$
ⓑ $x = 11$
ⓒ $x = −3$

How did it go?

PreviousMultiply and Divide Integers: example 3.59 Next Solve Equations Using Integers; The Division Property of Equality: example 3.61

From Prealgebra (1st edition) by OpenStax (Rice University), section 3.5, 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.