Question

Solve the inequality for x. Show each step of the solution.10x > 2(8x – 3) – 18

Answer 1

Answer: x<4

Given the inequality:

`10x>2(8x-3)-18`

We want to solve the inequality for x.

First, distribute the bracket on the right side of the inequality.

`\begin{gathered} 10x>2(8x)-2(3)-18 \\ 10x>16x-6-18 \\ 10x>16x-24 \end{gathered}`

Next, subtract 10x from both sides of the inequality.

`\begin{gathered} 10x-10x>16x-10x-24 \\ 0>6x-24 \end{gathered}`

Add 24 to both sides of the inequality.

`\begin{gathered} 0+24>6x-24+24 \\ 24>6x \end{gathered}`

Divide both sides of the inequality by 6.

`\begin{gathered} (24)/(6)>(6x)/(6) \\ 4>x \\ \implies x<4 \end{gathered}`

The solution to the inequality is x<4.