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)`

Step-by-step 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} \\ (3x)/(3)>(9)/(3) \\ x>3 \end{gathered}`

so, the solution of inequality 1 is

`x>3`

Step 2

solve inequality 2

`\begin{gathered} -2x\ge6 \\ (-2x)/(-2)\leq(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