\(\displaystyle bx-cx=x-2\)

Subtract to move all x terms to the same side:

\(\displaystyle bx-cx-x=-2\)

Factor out an x:

\(\displaystyle x(b-c-1)=-2\)

Divide to isolate x completely:

\(\displaystyle \mathbf{x=\frac{-2}{b-c-1}}\)

\(\displaystyle \sqrt{2x-4x}=\sqrt{x-2}\)

Square both sides to remove the radicals:

\(\displaystyle 2x-4x=x-2\)

Combine x terms:

\(\displaystyle -2x=x-2\)

Combine x terms to one side by subtracting:

\(\displaystyle -3x=-2\)

Isolate x completely:

\(\displaystyle x=\frac{2}{3}\)

Find the solution to the following equation.

\(\displaystyle 9x+23=59\)

To find the solution of this equation, we need to find the value for x, which makes the given equation true.

We do this by working backwards and manipulating the equation.

The easiest first step would probably be to subtract 23 from both sides:

\(\displaystyle 9x+23(-23)=59(-23)\)

By doing so, we can simplify the equation to get:

\(\displaystyle 9x=36\)

Next, simply divide both sides by 9 to get the answer!

\(\displaystyle 9x\div 9=36\div9\)

So we get:

\(\displaystyle x=4\)

Given the following equation, find the value of  \(\displaystyle b^3\) 

\(\displaystyle 355=7b+12\)

To find the value of \(\displaystyle b^3\), we first need to find the value of b

Let's begin by subtracting 12

\(\displaystyle 355(-12)=7b+12(-12)\)

Simplify

\(\displaystyle 343=7b\)

Finally, divide by 7

\(\displaystyle b=\frac{343}{7}=49\)

But, we need \(\displaystyle b^3\)

So:

\(\displaystyle b^3=49^3=117649\)

\(\displaystyle 27x-9=-18\)

Add 9 to both sides:

\(\displaystyle 27x=-9\)

Divide both sides by 27:

\(\displaystyle \mathbf{x=-\frac{1}{3}}\)

\(\displaystyle 27x-9=-18\)

Add 9 to both sides:

\(\displaystyle 27x=-9\)

Divide both sides by 27:

\(\displaystyle \mathbf{x=-\frac{1}{3}}\)

Let's set-up an equation. 

\(\displaystyle .25x+.10=3.35\) \(\displaystyle x\) represents the amount of bagels. After subtracting \(\displaystyle .10\) on both sides and dividing by \(\displaystyle 0.25\), our answer should be \(\displaystyle 13\) bagels.

Let's set-up an equation. 

\(\displaystyle 2+0.3x=21.80\) \(\displaystyle x\) how many fifth miles the taxi charges. After subtracting \(\displaystyle 2\) on both sides and dividing by \(\displaystyle 0.3\), our answer should be \(\displaystyle 66\). But of course, this is not the final answer because that's how many times the taxi charges for every fifth mile. So \(\displaystyle 66*\frac{1}{5}=13.2\) miles.

Since the person has traveled  \(\displaystyle 600\) miles and each mile uses \(\displaystyle \frac{1}{40}\) gallon, we can determine how many gallons used.  \(\displaystyle \frac{600}{40}=15\) gallons used. Since a tank holds \(\displaystyle 20\) gallons, we subtract \(\displaystyle 20\) and \(\displaystyle 15\) to get \(\displaystyle 5\) gallons. 

Let's set-up an equation.

\(\displaystyle 300-2x=180\) \(\displaystyle x\) represents how many times he lost the \(\displaystyle 2\) pounds. By subtracting \(\displaystyle 300\) on both sides and dividing by \(\displaystyle -2\) later, we get \(\displaystyle 60\). That's not our answer as he loses weight every five days. So we do \(\displaystyle 60*5=300\) days.