Question

1. Here is an inequality below: Select ALL of the values that are a solutionto the inequality.*72 +62<3r+2X=-3X-2X = -1X=0x= 1x = 2X = 3

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given inequality

`(7x+6)/(2)\le3x+2`

STEP 2: Solve for x

`\begin{gathered} (7x+6)/(2)\le3x+2 \\ \mathrm{Multiply\: both\: sides\: by\: }2 \\ 7x+6\le2(3x+2) \\ 7x+6\le\: 6x+4 \\ \mathrm{Subtract\: }6\mathrm{\: from\: both\: sides} \\ 7x+6-6\le\: 6x+4-6 \\ \text{By simplification,} \\ 7x\le\: 6x-2 \\ \mathrm{Subtract\: }6x\mathrm{\: from\: both\: sides} \\ 7x-6x\le\: 6x-2-6x \\ x\le\: -2 \end{gathered}`

STEP 3: Select the values that are a solution to the inequality

`\begin{gathered} \text{ Since }x\le-2,\text{ this means that x is less than or equal to -2} \\ \text{This implies that all values less than or equal to 2 are a solution to the inequality} \\ \text{Looking at the options, the values that are less than or equal to 2 are:} \\ x=-3,x=-2 \end{gathered}`

Hence, the values that are a solution to the inequality are: