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Chapter 1: Q46. (page 50)

Solve each inequality. Graph the solution set on a number line.

46. -1<3a+2<14

Short Answer

Expert verified

Solution set of inequality is a|-1<a<4.

Solution set on number line is

Step by step solution

01

- Write properties of inequality.

Properties of inequalities are written in following table:

02

- Solve −1<3a+2<14.

To solve given inequality, use subtraction and division properties of inequality. Subtract 2 from each part then divide each part by 3 and simplify.

鈭�1鈭�2<3a+2鈭�2<14鈭�2鈭�33<3a3<123鈭�1<a<4

Thus, solution is -1<a<4.

03

– Graph the solution set.

Assolution set of the inequality is all real numbers greater than -1 or less than 4.

The solution set is, a|-1<a<4.

Open circles on -1 and 4 shows these points are excluded in the solution set.

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