Question

Show your steps for full credit. Show your answer on a number line and in interval notation

8 ≤ 2m – 4 < 16 ​​​​

Answer 1

`\large \bf \implies{(6,10)}`

Explanation:

Step 1) : Solve the inequality

`\bf \longrightarrow{8 \leqslant 2m - 4 < 16}`

Separate compound inequalities into system of inequalities

`\begin{cases}2m - 4 \geqslant 8 \\2m - 4 < 16\end{cases}`

`\sf\underline{ \underline{2m - 4 \geqslant 8 \: and \: 2m - 4 < 16}}`

`1) \: \: \: \: \: \large\boxed{ \tt2m - 4 \geqslant 8}`

• Rearrange variables to the left side of the equation

`\bf \longrightarrow2m \geqslant 8 + 4`

• Calculate the sum or difference

`\bf \longrightarrow2m \geqslant 12`

• Divide both sides of the inequality by the coefficient of variable

`\bf \longrightarrow \: m \geqslant (12)/(2)`

• Cross out the common factor

`\bf \longrightarrow \: m \geqslant 6`

`2) \: \: \: \: \: \large \boxed{ \sf2m - 4 < 16}`

• Rearrange variables to the left side of the equation

`\bf \longrightarrow2m < 16 + 4`

• Calculate the sum or difference

`\bf \longrightarrow2m < 20`

• Divide both sides of the inequality by the coefficient of variable

`\bf \longrightarrow \: m < (20)/(2)`

• Cross out the common factor

`\bf \longrightarrow \: m < 10`

`\pink{ \rule{7cm}{0cm}}`

`\bf \longrightarrow \: m \geqslant 6 \: and \: m < 10`

• Find the intersection

`\bf \longrightarrow \boxed{ \sf6 \leqslant m < 10}`

Step 2) : Graph on a number line attached above

Step 3) : Express solution set in interval notation

`\bf \longrightarrow {\boxed {\underline {\underline{{( \bold{6,10)}}}}}}`