Question

I need to solve a multistep inequality, show my work and check my answer1.) -3x + 14 ≥ 3 - 2x2.) 8 (1/2x -1/4 ) ≤ 14

Answer 1

Step-by-step explanation

Given the inequality

`-3x+14\ge3-2x`

We can find the solution below;

`\begin{gathered} -3x+14\ge3-2x \\ \text{subtract 14 from both sides} \\ -3x+14-14\ge3-2x-14 \\ -3x\ge-2x-11 \\ \mathrm{Add\: }2x\mathrm{\: to\: both\: sides} \\ -3x+2x\ge-2x+2x-11 \\ -x\ge-11 \\ \mathrm{Multiply\: both\: sides\: by\: -1\: }\mleft(\mathrm{reverse\: the\: inequality}\mright) \\ x\le11 \end{gathered}`

Answer:

`\begin{bmatrix}\mathrm{Solution\colon}\: & \: x\le\: 11\: \\ \: \mathrm{Interval\: Notation\colon} & \: (-\infty\: ,\: 11\rbrack\end{bmatrix}`