Question

Which of the followingrepresents this inequality?|4x – 61 > 10

Answer 1

Given the absolute inequality below:

`\lvert4x-6\rvert>10`

From the absolute law,

`\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}`
`\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ (4x)/(4)>(16)/(4) \\ \Rightarrow x>4 \end{gathered}`
`\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ (4x)/(4)<-(4)/(4) \\ \Rightarrow x<-1 \end{gathered}`

Plotting the solution to the inequality, we have the line graph of the inequality to be

Hence, the correct option is D.