Originally Posted by

**o_O** my work below:

step 1: -6r-6 < or = to -4r+8

step 2: -6+4r < or = to 8+6

step 3: -2r < or = to 14/2

step 4: -2r div -2r < or = to 7

Answer: r > or = -7

Your work is fine with a few minor technicalities. From going to step 2 to step 3, your inequality would not be true as it seems like you 'randomly' divided by 2 but I presume you're just getting ahead of yourself and was meant for step 3 to step 4.

Also, I think you meant to divide both sides by -2 not -2**r** as you would end up with: $\displaystyle \frac{-2r}{{\color{blue}-2r}} \leq \frac{14}{{\color{blue}-2r}} \: \: \Rightarrow \: \: -2 \geq -\frac{7}{r}$ which isn't necessary.

In summary:

$\displaystyle \text{Step 3: } -2r \leq 14$ (Didn't divide by 2 **yet**. Remember: What you do to one side you do to the other)

$\displaystyle \text{Step 4: }\frac{-2r}{{\color{blue}-2}} \leq \frac{14}{{\color{blue}-2}}$

$\displaystyle \text{Answer: } r \geq -7$