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Chapter 2: Q. 655 (page 299)

In the following exercises,, solve each inequality, graph the solution on the number line, and write the solution in interval notation.

3c鈭�10(c鈭�2)<5c+16.

Short Answer

Expert verified

The solution for the given inequality is,c>13.

A graph for the solution on the number line is,

From the number line, the obtained interval notation is,13,鈭�.

Step by step solution

01

Step 1. Given information

3c鈭�10(c鈭�2)<5c+16.

02

Step 2. First solve the given inequality.

Simplify each side as much as possible by using the distributive property.

3c鈭�10(c鈭�2)<5c+163c-10c+20<5c+16-7c+20<5c+16

Add 7con both the sides of the equation to collect the variable on the right side and then simplify it.

-7c+7c+20<5c+7c+1620<12c+16

03

Step 3. Now subtract 16 on the both sides of the equation to collect the constants on the left side and then simplify it.

20-16<12c+16-164<12c412<cc>13

04

Step 4. Now graph the solution on the number line.

Write the solution in the interval notation.

From the number line, the obtained interval notation is,13,鈭�.

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