Answer:
[tex]x < -3\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]-6x+22\frac{1}{4}+2x > 9\frac{3}{4} +16\frac{1}{2}[/tex]
Required
Solve for x
[tex]-6x+22\frac{1}{4}+2x > 9\frac{3}{4} +16\frac{1}{2}[/tex]
Collect Like Terms
[tex]-6x+2x > 9\frac{3}{4} +16\frac{1}{2}-22\frac{1}{4}[/tex]
[tex]-4x > 9\frac{3}{4} +16\frac{1}{2}-22\frac{1}{4}[/tex]
Convert all fractions to improper fractions
[tex]-4x > \frac{39}{4} +\frac{33}{2}-\frac{45}{4}[/tex]
Take LCM
[tex]-4x > \frac{39+66- 45}{4}[/tex]
[tex]-4x > \frac{60}{4}[/tex]
[tex]-4x > 15[/tex]
Divide through by -4; When an inequality is divided by a negative number, the inequality changes.
[tex]\frac{-4x}{-4} < \frac{15}{-4}[/tex]
[tex]x < \frac{15}{-4}[/tex]
[tex]x < -\frac{15}{4}[/tex]
Convert to improper fraction
[tex]x < -3\frac{3}{4}[/tex]
