Question

7Which of the graphs below shows the solution set for −36≤2x+4(x−3)?

Answer 1

Given:

There are given that inequality:

`-36\leq2x+4(x-3)`

Step-by-step explanation:

According to the question:

We need to solve the above-given inequality:

`\begin{gathered} -36\leqslant2x+4(x-3) \\ -36\leqslant2x+4x-12 \end{gathered}`

Then,

`\begin{gathered} -36\leqslant2x+4x-12 \\ -36\leqslant6x-12 \end{gathered}`

Then,

`6x-12\ge-36`

Then,

Add 12 on both sides of the equation:

`\begin{gathered} 6x-12\geqslant-36 \\ 6x-12+12\geqslant-36+12 \\ 6x\ge-24 \end{gathered}`

Then,

Divide by 6 on both sides of the equation:

So,

`\begin{gathered} 6x\geqslant-24 \\ (6x)/(6)\geqslant(-24)/(6) \\ x\ge-4 \end{gathered}`

We can see that the value of x is greater than and equal to -4.

Final answer:

Hence, the correct option is B.