To combine like terms, combine the numbers as you would a normal addition or subtraction problem:

Therefore, = 8x - 8y.

To solve for X, isolate X on one side of the equation.  In this case, we are required to subtract one number from X.  When we add that number to both sides of the equation, we isolate X and obtain our answer.  

We need to translate this word sentence into algebra: The square root of the sum of twice a number and five is equal to the square of the difference between that number and two.

The words "is equal to" denote the equal sign. Everything before it will be to the left of the equal sign, and everything after will be on the right.

The first half of the sentence says "The square root of the sum of twice a number and five." We can represent twice the number as 2n. The sum of twice the number and five can be represented by 2n + 5, because "sum" denotes addition. We need to take the square root of the quantity 2n + 5, which we can write as . The left side of the equation will be .

On the right side, we need to find the square of the difference between n and 2. "Difference" tells us to subtract, so we can represent this as n - 2. If we take the square of this quantity, we can represent this as . The right side of the equation is .

Putting both sides together with the equal sign, the entire equation is  .

The answer is  .

The cost per attendee, , must be multiplied by the total number of attendees and then added to the base cost, , to obtain the total cost.

In order to sovle for , subtract  from both sides:

To find how much additional money Sarah would make by applying the discount, find the difference between her earnings in a normal month and a month where the discount is applied. In a normal month, multiply the normal price by the normal quantity sold to find the normal earnings:

To find earnings at the discounted price, first calculate how much each necklace will cost with the % discount. To do this, subtract the amount discounted (calculated by percent as a fraction of  multiplied by the original price) from the original price.

If  necklaces are sold at the new discounted price of  each, multiply these together to find the total earnings with the discount.

Finally, subtract the earnings without the discount from the earnings with the discount to find the additional money made by applying the discount.

The statement "A jar of Verde Salsa costs more than a jar of Rojo Salsa" can be tested by comparing the price per jar of each salsa.

 versus 

The statement is false since the price of Rojo per jar is greater. 

The remaining statements above can all be proven true or false by finding the price per ounce of each salsa.

Rojo Salsa is on sale at a price of  for  jars of  ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:

 for Rojo Salsa.

Verde Salsa is on sale at a price of  for  jars of  ounces each. The following operations can be used to determine the cost of Verde Salsa per ounce.

 for Verde Salsa.

The only true statement is "An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa."

To solve this word problem, set up an algebraic equation, putting  in for the unknown value of the second shirt. The equation is  because we know the cost of the two shirts will total .

To solve for , subtract  from each side. This results in .

Convert 15% to a decimal.

Let the original price equal . The discount will be 15% of . Subtracting the discount from the original price will equal the amount paid, $12.

Using this equation, we can solve for .

If this is a square fence, then each of the four sides will be equal.

The fence in question will become the perimeter of that square.

Since  when working with a square, for this problem .