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

`x < -3(3)/(4)`

Explanation:

Given

`-6x+22(1)/(4)+2x &gt; 9(3)/(4) +16(1)/(2)`

Required

Solve for x

`-6x+22(1)/(4)+2x &gt; 9(3)/(4) +16(1)/(2)`

Collect Like Terms

`-6x+2x &gt; 9(3)/(4) +16(1)/(2)-22(1)/(4)`

`-4x &gt; 9(3)/(4) +16(1)/(2)-22(1)/(4)`

Convert all fractions to improper fractions

`-4x &gt; (39)/(4) +(33)/(2)-(45)/(4)`

Take LCM

`-4x &gt; (39+66- 45)/(4)`

`-4x &gt; (60)/(4)`

`-4x &gt; 15`

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

`(-4x)/(-4) &lt; (15)/(-4)`

`x &lt; (15)/(-4)`

`x &lt; -(15)/(4)`

Convert to improper fraction

`x < -3(3)/(4)`