Question

−7x+1≥22 OR −10x+41≥81

Answer 1

`x\leq -3`

Explanation:

We have been given a compound inequality. We are supposed to solve our given inequality.

`-7x+1\geq 22\text{ or }-10x+41\geq 81`

First of all, we will solve both of our given inequalities separately, then we will combine the solution of both inequalities.

`-7x+1-1\geq 22-1`

`-7x\geq 21`

we know dividing or multiplying inequality by a negative number flips inequality.

`(-7x)/(-7)\leq (21)/(-7)`

`x\leq -3`

`-10x+41\geq 81`

`-10x+41-41\geq 81-41`

`-10x\geq 40`

`(-10x)/(-10)\leq (40)/(-10)`

`x\leq -4`

Upon merging overlapping intervals, the solution for our given inequality would be
`x\leq -3`.

Answer 2

`-7x+1\geq22\qquad\text{subtract 1 from both sides}\\\\-7x\geq21\qquad\text{change the signs}\\\\7x\leq-21\qquad\text{divide both sides by 7}\\\\x\leq-3\\-----------\\-10x+41\geq81\qquad\text{subtract 41 from both sides}\\\\-10x\geq40\qquad\text{change the signs}\\\\10x\leq-40\qquad\text{divide both sides by 10}\\\\x\leq-4\\------------\\\\x\leq-3\ or\ x\leq-4\ therefore\ x\leq-3`