How do you solve the inequality -5q+9>24?

3 Answers
May 22, 2018

See a solution process below:

Explanation:

First, subtract color(red)(9) from each side of the inequality to isolate the q term while keeping the inequality balanced:

-5q + 9 - color(red)(9) > 24 - color(red)(9)

-5q + 0 > 15

-5q > 15

Next, divide each side of the inequality by color(blue)(-5) to solve for q while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

(-5q)/color(blue)(-5) color(red)(<) 15/color(blue)(-5)

(color(blue)(cancel(color(black)(-5)))q)/cancel(color(blue)(-5)) color(red)(<) -3

q color(red)(<) -3

May 22, 2018

q<-3.

Explanation:

Solving an inequality is almost exactly like solving an equality, and for the most part you can treat it as such while solving it, except for one additional rule: whenever you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. For example, > would go to <, <= to >= and vice versa. If you wish to know why you must do this, read the next paragraph; otherwise, you may skip it.

The reason this rule arises is because of how the number line works. Observe that on the standard number line, numbers go smallest (-oo) to largest (oo) from left to right, with 0 in the exact center. If we write a< b we mean to say that a is farther to the right than a. But, if we consider -a and -b, we will notice that -a < -b is false because -a is farther to the right than -b.

Now we solve your inequality:

-5q+9>24.

First we subtract 9 from both sides to get,

-5q+9-9>24-9 rArr -5q>15.

Now we divide both sides by -5, flipping the inequality:

(-5q)/-5>(15)/-5 rArr q<-3.

May 22, 2018

q< -3

Explanation:

"isolate "-5q" by subtracting 9 from both sides"

rArr-5q> 24-9

rArr-5q> 15

"divide both sides by "-5

color(blue)"remember to reverse the sign as a consequence"

rArrq< -3