Respuesta :

ProfessorAlvarez

[tex]\text{Hello there!}\\\\\text{Solve for q:}\\\\q + 12 - 2 (q - 22) > 0\\\\\text{Distribute the -2 to the variables inside the parenthesis}\\\\q + 12 - 2q +44 > 0\\\\\text{Combine like-terms}\\\\-q+56>0\\\\\text{Subtract 56 from both sides}\\\\-q>-56\\\\\text{Divide both sides by -1. Flip the inequality since you're dividing by}\\\text{a negative}\\\\\boxed{q<56}[/tex]

Answer:

q<56

Step-by-step explanation:

To solve this problem, first, you have to isolate it on one side of the equation. Isolate q on one side of the equation.

q+12-2(q-22)>0

q+12-2(q-22)-12>0-12 (First, subtract by 12 from both sides.)

0-12 (Solve.)

q-2(q-22)>-12

DISTRIBUTIVE PROPERTY:

A(B+C)=AB+AC

A(B-C)=AB-AC

-2(q-22) (Expand.)

-2*q=-2q

-2*22=44

-2q+44

q-2q+44>-12

q-2q=-q (Add & subtract the numbers from left to right.)

-q+44>-12

-q+44-44>-12-44 (Subtract by 44 from both sides.)

-12-44 (Solve.)

-12-44=-56

-q>-56

(-q)(-1)<(-56)(-1) (Multiply -1 from both sides.)

(-56)(-1) (Solve.)

(-56)(-1)=56

q<56

In conclusion, the correct answer is q<56.

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