# solve using addition and multiplication principles

• Jun 8th 2008, 06:23 AM
Mr.Huge
solve using addition and multiplication principles
Did I do this correct? Its been about 10 years since i been to school and am having some issues remembering how to do a lot of this stuff.

-6r-6 is less than or = to -2(2r-4)

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

Let me know if i did this correct sorry i dont know how to type the correct characters for less than or = to or divide etc.

Mr.H
• Jun 8th 2008, 08:29 AM
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 -2r 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)
$\displaystyle \text{Step 4: }\frac{-2r}{{\color{blue}-2}} \leq \frac{14}{{\color{blue}-2}}$
$\displaystyle \text{Answer: } r \geq -7$
• Jun 8th 2008, 12:45 PM
Mr.Huge
Quote:

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 -2r 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)
$\displaystyle \text{Step 4: }\frac{-2r}{{\color{blue}-2}} \leq \frac{14}{{\color{blue}-2}}$
$\displaystyle \text{Answer: } r \geq -7$

Yes,

I also divded in my head the 14/2 by -2 i should have shown that work as part of step 4 but i am on the right track here which is good thank you for your response.

Mr.Huge