Question

Need help finding the answer step by stepa. add 3 to both sidesb. subtract 5 to both sidesc. multiply 3 to both sidesd. multiply -2 to both sides

Answer 1

`\begin{gathered} \text{Given} \\ 3x+10<8 \end{gathered}`

Part A: adding 3 to each side

Add 3 to both sides and simplify the inequality.

`\begin{gathered} 3x+10<8 \\ 3x+10+3<8+3 \\ 3x+13<11 \end{gathered}`

Part B: subtracting 5 to each side

Subtract 5 to both sides and simplify the inequality

`\begin{gathered} 3x+10<8 \\ 3x+10-5<8-5 \\ 3x+5<3 \end{gathered}`

Part C: multiply 3 to each side

Multiply both sides of the inequality by 3

`\begin{gathered} 3x+10<8 \\ (3x+10)\cdot3<(8)\cdot3 \\ 9x+30<24 \end{gathered}`

Part D: multiply -2 to each side

Recall that when multiplying or dividing both sides by a negative number, the inequality in the middle is flipped.

Multiplying by -2 we have the following

`\begin{gathered} 3x+10<8 \\ (3x+10)\cdot-2>(8)\cdot-2 \\ -6x-20>-16 \end{gathered}`