First, solve for x:

11 + 3x = 29

29 – 11 = 3x

18 = 3x

x = 6

Then, solve for 2x:

2x = 2 * 6 = 12

Create 3 separate equations to solve for each variable separately.

1) 2x = 48

2) 3y = 48

3) 6z = 48

x = 24

y = 16

z = 8

x * y * z = 3072

We must solve each absolute value equation separately for x and y. Remember that absolute values will always give two different values. In order to find these two values, we must set our equation to equal both a positive and negative value.

In order to solve for x in  3|x – 2| = 12,

we must first divide both sides of our equation by 3 to get |x – 2| = 4.

Now that we no longer have a coefficient in front of our absolute value, we must then form two separate equations, one equaling a positive value and the other equaling a negative value.

We will now get x – 2 = 4

and 

x – 2 = –4.

When we solve for x, we get two values for x:

x = 6 and x = –2.

Do the same thing to solve for y in the equation |y + 4| = 8

and we get

y = 4 and y = –12.

This problem asks us to solve for all the possible solutions of |x - y|.

Because we have two values for x and two values for y, that means that we will have 4 possible, correct answers.

|6 – 4| = 2

|–2 – 4| = 6

|6 – (–12)| = 18

|–2 – (–12)| = 10

Cross multiplying leaves $\displaystyle 3x+6=3x$, which is not possible.

In evaluating, we can simply plug in 4 and 2 for $\displaystyle x$ and $\displaystyle y$ respectively. We then get $\displaystyle 16-16=0$.

The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives

$\displaystyle \$0.20(x-10)+5$.

If we take the units and look at division, $\displaystyle miles/(miles/hour)$ will yield hours as a unit. Therefore the answer is $\displaystyle b/c$.

In general, $\displaystyle distance=rate\times time$. 

The distance is the same going and coming; however, the head wind affects the rate.  The equation thus becomes $\displaystyle (r-25)\times 5=(r+25)\times 4$.

Solving for $\displaystyle r$ gives $\displaystyle r=225\ mph$.

Pure water is 0% and pure solution 100%.  Let $\displaystyle x$ = water to be added.

$\displaystyle V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$  in general where $\displaystyle V$ is the volume and $\displaystyle P$ is the percent.

So the equation to solve becomes $\displaystyle x(0)+2(0.90)= (x+2)(0.50)$

and $\displaystyle x=1.6\ L$

This problem is a good example of the substitution method of solving a system of equations.  We start by rewritting the first equation in terms of $\displaystyle x$ to get $\displaystyle x=14-2y$ and then substutite the $\displaystyle x$ into the second equation to get

$\displaystyle 2(14-2y)+y=13$. 

Solving this equation gives $\displaystyle y=5$ and substituting this value into one of the original equations gives $\displaystyle x=4$, thus the correct answer is $\displaystyle (4,5)$.