Question

Solve the inequality and express your answer in intervalvenation use decimal form for numeric values

Answer 1

Given:

`(20)/(4)<(z+7)/(2)<(25)/(4)`

Required :

To solve this

Step-by-step explanation:

`\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ (z+7)/(2)>(20)/(4)\text{ }(z+7)/(2)<(25)/(4) \\ \\ reduce\text{ the fraction} \\ \\ (z+7)/(2)>5\text{ or z+7>2}*5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}`
`\begin{gathered} (z+7)/(2)<(25)/(4) \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4*(z+7)/(2)<4*(25)/(4) \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<(11)/(2) \end{gathered}`[tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:

3