Question

Solve the inequality 1/3x+3/4<1/2x and describe the graph of the solutions. Show all work

Answer 1

Our goal is to isolate the x to one side of the inequality. We kind of treat the inequality sign like an equal sign and solve for x
The first step is to bring all the x's to one side of the inequality
So we would begin by subtracting a 1/3x from both sides
\(\large \frac{1}{3}x- \frac{1}{3}x+ \frac{3}{4}<\frac{1}{2}x-\frac{1}{3}x\)

\( \large \frac{3}{4}<\frac{1}{2}x-\frac{1}{3}x\)

\( \large \frac{3}{4}<\frac{1}{6}x\)

Answer 2

Ya with me so far?

Answer 3

yes

Answer 4

So now in order to isolate the x we multiply both sides by 6

\( \large \frac{3}{4}*\small{6}< \small{6}*\large\frac{1}{6}x \)

\( \large \frac{18}{4}<x\)

\( \large 4.5<x\)

Answer 5

ok

Answer 6

Any questions so far and can you explain to me what x >4.5 means?

Answer 7

x is greater than 4.5?

Answer 8

Yup

Answer 9

ok

Answer 10

thanks

Answer 11

ok

Answer 12

whooopsssss I meant
So basically in order for this inequality to be true x must be greater than 4.5

Answer 13

ohh ok