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Chapter 5: Q13. (page 323)

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

6+h<1

Short Answer

Expert verified

The solution of the given inequality6+h<1 is h<鈭�5.

The graph of the solution of the given inequality6+h<1 that is graph ofh<鈭�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鈭�c>b鈭�c.

(ii) If a<b, then a鈭�c<b鈭�c.

02

Step 2. Solve the given inequality 6+h<1.

The solution of the given inequality6+h<1is:

localid="1647495432794" 6+h<16+h鈭�6<1鈭�6h+6鈭�6<鈭�5h<鈭�5(byusingsubtractionpropertyofinequality)

Therefore, the solution of the given inequality6+h<1is h<鈭�5.

03

Step 3. Draw the graph of the inequality h<−5.

The graph of the solution of the given inequality6+h<1that is graph ofh<鈭�5is:

It can be noticed that at h=鈭�5, there is open circle because鈭�5 is not included in the inequality h<鈭�5.

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