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Chapter 1: Q45. (page 50)

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

45. 82x-1>11x-17

Short Answer

Expert verified

Solution set of inequality is (-1.8,+鈭�).

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 82x−1>11x−17.

To solve given inequality, use subtraction, addition and division properties of inequality. Expand the left-hand side. Add 8 on each side then subtract 11xfrom each side and divide each side by 5 and simplify.

16x鈭�8>11x鈭�1716x鈭�8+8>11x鈭�17+816x鈭�11x>11x鈭�9鈭�11x5x5>鈭�95x>鈭�1.8

Thus, solution is x>-1.8.

03

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers greater than -1.8.

Write the solution set in interval notation.

(-1.8,+鈭�)

04

– Graph the solution set.

Open circle on-1.8 shows this point is excluded in the solution set.

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