Question

hi can u help w a few math problems? "solve the compound inequality. 4x-6 (less than equal to sign) 14 and 3x +5 (greater than to sign) -1.

Answer 1

-2 ≤ x ≤ 5

Step-by-step explanation:

Given the compound inequalities:

`4x-6\le14\text{ and 3}x+5\ge-1`

First, solve each of the inequalities separately:

`\begin{gathered} 4x-6\le14 \\ \text{Add 6 to both sides} \\ 4x-6+6\le14+6 \\ 4x\le20 \\ \text{Divide both sides by 4} \\ (4x)/(4)\le(20)/(4) \\ x\le5 \end{gathered}`

Similarly, solve the second one:

`\begin{gathered} 3x+5\ge-1 \\ \text{Add -5 to both sides} \\ 3x+5-5\ge-1-5 \\ 3x\ge-6 \\ \text{Divide both sides by }3 \\ (3x)/(3)\ge-(6)/(3) \\ x\ge-2 \\ \implies-2\le x \end{gathered}`

The solution to the compound inequality is:

`-2\le x\le5`

The graph of the solution is attached below: