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In $3-14,$ solve and check each inequality.$$\frac{a}{4}>\frac{a}{2}+6$$

$\{a | a<-24\}$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 8

Solving Rational Inequalities

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Campbell University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:05

In $3-14,$ solve and check…

06:10

03:36

00:50

Solve each inequality.…

00:52

Solve each inequality.

00:25

Solve each equation or ine…

08:23

03:42

05:58

we're going to be solving the inequality. A over four is greater than ever to plus six. Let's get started. So first off, what I want to do here is get the A's all in one place. So I'm going to be subtracting and a over to from both sides, giving us on the left, a over four minus a over to eyes greater than six. And now we're going to get some common denominators on the left that we can combine these two fractions. So we're going to be multiplying the second term. That is that a over two by 2/2, giving us a over four minus two a over four eyes greater than six so we can subtract that giving us negative a over four is greater than six. Then we can multiply across by this four. Giving us negative A is greater than 24. Ah, and finally, we can divide over by this negative. Now the important thing to remember here is that divided by a negative will flip the sign or flip the direction of the inequality around. Giving us A is less than on negative 24 so the answer's here is the set of all a such that a is less than negative. 24

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