Question

Kuta Software - Infinite Algebra 2 Wave Sudha saba los) Compound Inequalities 23 Solve each compound inequality and graph its solution. 1) n+13 3 or an

Answer 1

Part 9

solve the first inequality

$9-12r\ge-99$

solve for r

$\begin{gathered} -12r\ge-99-9 \\ -12r\ge-108 \\ mu\text{ltiply by -1 both sides} \\ 12r\leq\text{ 108} \\ r\leq9 \end{gathered}$

the first solution is the interval (-infinite, 9}

Solve the second inequality

we have

$\begin{gathered} -2r-4\text{ }<-12 \\ -2r<-12+4 \\ -2r<-8 \\ m\mu\text{ltiply by -1 both sides} \\ 2r>8 \\ r>4 \end{gathered}$

the solution is the interval (4, infinite)

therefore

the solution of the compound inequality is

(-infinite, 9} ∩ (4, infinite)=(4,9}

All real numbers greater than 4 and less than or equal to 9