Question

Solve –2|3x – 12|>-54 and graph the solution on a number line.

Answer 1

Step-by-step explanation:

`-2|3x-12|>-54`

divide both sides by -2:

`\begin{gathered} (-2|3x-12|)/(-2)>(-54)/(-2) \\ \text{when you divide an inequality by a negative nuber the sign changes} \\ \text{from > to < in this case} \\ |3x-12|\text{ < 27} \end{gathered}`
`\begin{gathered} |3x-12|<\text{ 27 is the same as:} \\ (3x\text{ -12) <27 or (3x -12) < -27} \end{gathered}`

solving each seperately:

`\begin{gathered} (3x\text{ -12) <27} \\ \text{add 12 to both sides:} \\ 3x\text{ -12 + 12 < 27 + 12} \\ 3x\text{ + 0 < 39} \\ 3x\text{ < 39} \\ (3x)/(3)<(39)/(3) \\ x\text{ < 13} \end{gathered}`
`\begin{gathered} (3x\text{ - 12) < -27} \\ \text{add 12 to both sides:} \\ 3x\text{ -12 + 12 < -27 + 12} \\ 3x\text{ + 0 < -15} \\ 3x\text{ < -15} \\ \text{divide both sides by 3:} \\ (3x)/(3)<(-15)/(3) \\ x\text{ < -5} \end{gathered}`