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Chapter 5: Q12. (page 323)

Solve each inequality. Then graph it on a number line.

x+8≤3

Short Answer

Expert verified

The solution of the given inequalityx+8≤3 is x≤−5.

The graph of the solution of the given inequalityx+8≤3 that is graph ofx≤−5 is:

Step by step solution

01

Step 1. Write the subtraction property of inequalities.

The subtraction property of inequalities states that if the same number is subtracted from each side of a true inequality, the resulting inequality is also true that is:

(i) If a>b, then a−c>b−c.

(ii) If a<b, then a−c<b−c.

02

Step 2. Solve the given inequality x+8≤3.

The solution of the given inequality x+8≤3is:

localid="1647495544907" x+8≤3x+8−8≤3−8x≤−5(byusingsubtractionpropertyofinequality)

Therefore, the solution of the given inequality x+8≤3is x≤−5.

03

Step 3. Draw the graph of the inequality x≤−5.

The graph of the solution of the given inequality x+8≤3that is graph of x≤−5is:

It can be noticed that at x=−5, there is closed circle because−5 is included in the inequality x≤−5.

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