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Chapter 1: Q43. (page 50)

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

36-5a<12a-36

Short Answer

Expert verified

Solution set of inequality is (2,+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 36−5a<12a−36.

To solve given inequality, use subtraction and division properties of inequality. Expand the left-hand side. Add 36 on each side then add15a on each side and divide each side by 27 and simplify.

18鈭�15a+36<12a鈭�36+3654鈭�15a+15a<12a+15a5427<27a272<a

Thus, solution is 2<a.

03

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers greater than 2.

Write the solution set in interval notation.

(2,+鈭�)

04

– Graph the solution set.

Open circle on 2 shows this point is excluded in the solution set.

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Write expressions having values from one to ten using exactly four 4s. You may use any combination of the operation symbols +,-,脳,梅,and/or grouping symbols, but no other numbers are allowed. An example of such an expression with a value of zero is 4+4-4+4

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