# Multi-Step Linear Inequalities

• Feb 11th 2008, 01:28 PM
Nightfire
Multi-Step Linear Inequalities
i got every problem right on these things, except for ones involving Fractions. i thought i had it, but...
here's the ones i missed. (note: 1/2=one half, idk how to do fractions.) i tried to divide by the fraction, which went badly, and ended up with huge decimals...so i guess that wasnt right. (Surprised)
Also, i don't know how to do a Greater than or equal to, or a less than or equal to, sign, so i'm just going to use <(=) or >(=)

2/3x + 3 >(=) 11

6 >(=) 7/3x - 1

-1/2x + 3 < 7

• Feb 11th 2008, 01:39 PM
Aryth
Let's look at the first one:

$\displaystyle \frac{2}{3}x + 3 \geq 11$

First step, subtract three from both sides of the inequality using the rule:

"An equal quantity may be added to, (or subtracted from) both sides of an inequality without changing the inequality"

$\displaystyle \frac{2}{3}x \geq 8$

Now we have to multiply both sides by 3 using the rule:

"An equal positive quantity may multiply (or divide) both sides of an inequality without changing the inequality."

$\displaystyle 2x \geq 24$

Using the same rule above, we have to divide by 2 to isolate x:

$\displaystyle x \geq 12$

And there you go.

Another IMPORTANT rule is this:

"If both sides of an inequality are multiplied (or divided) by a negative quantity then the inequality is reversed"

I think you can solve the other two.
• Feb 11th 2008, 01:53 PM
Nightfire
ok, i think i got it, but just to point out.. you only subtracted 2 from the right side, so it would really be (at that point) 2/3x >(=) 8
thanks