Question

can you please explain how to get this answer solve the compound inequality 3x-4>5 or 1 -2x>=7

Answer 1

$(-\infty,3)\text{ }\cup\text{ }\lbrack3,\infty)$

Explanation

Step 1

solve the inequality 1

$\begin{gathered} 3x-4>5 \\ \text{add 4 in both sides} \\ 3x-4+4>5+4 \\ 3x>9 \\ \text{divide both sides by 3} \\ \frac{3x}{3}>\frac{9}{3} \\ x>3 \end{gathered}$

so, the solution of inequality 1 is

$x>3$

Step 2

solve inequality 2

$\begin{gathered} 1-2x\ge7 \\ \text{subtract 1 in both sides} \\ 1-2x-1\ge7-1 \\ -2x\ge6 \\ \text{divide both sides by -2( remember swap the sign when multiplying or dividing by a negative number)} \\ \end{gathered}$$\begin{gathered} -2x\ge6 \\ \frac{-2x}{-2}\leq\frac{6}{-2} \\ x\leq-3 \end{gathered}$

Step 3

finally, we have or, it means the solution is the union of the sets,

hence

solution

$\begin{gathered} x>3\text{ }\cup x\leq-3 \\ (-\infty,3)\text{ }\cup\text{ }\lbrack3,\infty) \end{gathered}$

x