Question

simplifying expressions in inequalities....-6x+22 1/4+2x>9 3/4 +16 1/2......i did this equation but when i plug in the numbers for x, it's false. the answer i got on the inequality is x<-1​

Answer 1

Answer:

$x < -3\frac{3}{4}$

Step-by-step explanation:

Given

$-6x+22\frac{1}{4}+2x > 9\frac{3}{4} +16\frac{1}{2}$

Required

Solve for x

$-6x+22\frac{1}{4}+2x > 9\frac{3}{4} +16\frac{1}{2}$

Collect Like Terms

$-6x+2x > 9\frac{3}{4} +16\frac{1}{2}-22\frac{1}{4}$

$-4x > 9\frac{3}{4} +16\frac{1}{2}-22\frac{1}{4}$

Convert all fractions to improper fractions

$-4x > \frac{39}{4} +\frac{33}{2}-\frac{45}{4}$

Take LCM

$-4x > \frac{39+66- 45}{4}$

$-4x > \frac{60}{4}$

$-4x > 15$

Divide through by -4; When an inequality is divided by a negative number, the inequality changes.

$\frac{-4x}{-4} < \frac{15}{-4}$

$x < \frac{15}{-4}$

$x < -\frac{15}{4}$

Convert to improper fraction

$x < -3\frac{3}{4}$