Start by breaking up the details.  Let $\displaystyle x$ be the unknown number.

Two times a number:  $\displaystyle 2x$

Is equal to:  $\displaystyle =$

One less than the number:  $\displaystyle x-1$

Combine all the terms.

The answer is:  $\displaystyle 2x=x-1$

To solve this question, break up the wording by parts.

Quantity of two less than a number:  $\displaystyle (x-2)$

Four times the quantity of two less than a number:  $\displaystyle 4(x-2)$

Is:  $\displaystyle =$

Eight times the number:  $\displaystyle 8x$

Combine the terms.

The answer is:  $\displaystyle 4(x-2)=8x$

To translate this into an expression, it's helpful to identify what the constant is in the problem. In other words, what is not changing no matter how many photos you print? In this case, it's the set-up fee $\displaystyle (25)$. Then, we identify where our variable will be coming into play. We don't know how many photos will be printed, so let's call the number of photos $\displaystyle p$. We know that it costs $\displaystyle .75$ per photo printed so that becomes $\displaystyle .75p$. Add those together to get your final expression: $\displaystyle .75p+25$.

The area of a rectangular is length times width. So,

If $\displaystyle A=LW$ and $\displaystyle A=24$. Then,

$\displaystyle LW=24$

The length of the pool is two feet less than twice the width, which means:

$\displaystyle L=2W-2$

Substitute $\displaystyle L$ in $\displaystyle LW=24$ with $\displaystyle 2W-2$:

$\displaystyle (2W-2)W=24$

so 

$\displaystyle 2W^{2}-2W=24$

You know that shirts sell for 15 dollars and jeans sell for 30 dollars.

The tricky part is knowing that you sold at least 200 dollars worth of merchandise.

This means that you could have sold more than 200 dollars, but no less than that.

This means that your answer is

$\displaystyle \small 15s+30j\geq 200$

The cost for p pounds of potatoes is 2.25p and the cost for q pounds of quinoa is 5.75q. The total amount Corey pays is the sum of the cost for potatoes and the cost for quinoa.

2.25p + 5.75q = 37.25

Recall the form for slope-intercept as follows.

$\displaystyle y=mx+b$

where $\displaystyle m$ represents the slope and $\displaystyle b$ is the y-intercept.

Given the equation in this question, first distribute the one fourth to both terms inside the parentheses.

$\displaystyle y+2 = \frac{1}{4}(x-4) = \frac{x}{4}-1$    

Next, subtract two from both sides to isolate y.

$\displaystyle y+2=\frac{x}{4}-1$

     $\displaystyle {\color{Red} -2}$            $\displaystyle {\color{Red} -2}$

This results in the slope-intercept form of the equation.

$\displaystyle y=\frac{x}{4}-3$

Knowing:

• $\displaystyle distance=rate*time$
• $\displaystyle x=rate_{BeetleA}$
• $\displaystyle time_A+time_B=time_{total}$

Beetle A: 

$\displaystyle time_A=\frac{distance}{rate}=\frac{30cm}{x}$

Beetle B: 

$\displaystyle time_B=\frac{distance}{rate}=\frac{90cm}{3x}$

Combined:

$\displaystyle time_A+time_B=time_{total}$

$\displaystyle \frac{30cm}{x}+\frac{90cm}{3x}=40sec$

Multiply each term by LCD (3x) to get:

$\displaystyle 90cm+90cm=120sec*x$

$\displaystyle \frac{180cm}{120}=x$

$\displaystyle x=\frac{3cm}{2sec}=1.5\frac{cm}{sec}$

Split up the sentence into parts.

Twice a number:  $\displaystyle 2x$

Six less than twice a number:  $\displaystyle 2x-6$

The square root of six less than twice a number:  $\displaystyle \sqrt{2x-6}$

Is equal to nine:  $\displaystyle \sqrt{2x-6}=9$

The answer is:  $\displaystyle \sqrt{2x-6}=9$

Break up the problem into parts.

Two times a number:  $\displaystyle 2x$

 The sum of two times a number and forty:  $\displaystyle 2x+40$

Is equal to sixteen:  $\displaystyle 16$

Combine the terms to form the equation.

The answer is:  $\displaystyle 2x+40=16$