Question

−8x+44≥60 AND−4x+50<58

Answer 1

Answer:

No Solution

Step-by-step explanation:

$-8x+44\geq 60 and  -4x+50<58$

WE solve each inequality separately then we combine the answers

$-8x+44\geq 60$

Subtract 44 from both sides

$-8x\geq 16$

Divide by $-8$ on both sides , when we divide by negatie number then we flip the inequality sign

$x \leq -2$

now solve the other inequality

$-4x+50<58$

Subtract 50 on both sides

$-4x<8$

Divide by $-4$

$x > -2$

Consider both inequlities

$x \leq -2$ and $x > -2$

There is no intersection between both inequalities

So no solution

Answer 2

Answer:

The set of inequalities have no solution.    

Step-by-step explanation:

We are given two inequalities:

$-8x+44\geq 60 \\-4x+50<58$

Solving the two inequalities, we have:

$-8x+44\geq 60\\-8x+44-44\geq 60-44\\-8x \geq 16\\\displaystyle\frac{-8x}{-8} \leq \frac{16}{-8}\\\\x \leq -2\\\text{In interval notation, we can write,}\\x \in (-\infty, -2]$

$-4x+50<58\\-4x +50-50 < 58-50\\-4x < 8\\\displaystyle\frac{-4x}{-4} > \frac{8}{-4}\\\\x > -2\\\text{In interval notion we can write,}\\x \in (-2, \infty)$

For the solution of both the inequalities, we have

$x \in (-\infty,-2] \cap (-2,\infty) = \phi$

Thus,the set of inequalities have no common solution, hence, no solution.