Factoring gives us (x + 2)(x + 3). This yields x = –2, –3.

You set up the equation and you get: (x/3) + 2 = 2x – 23.

Add 23 to both sides: (x/3) + 25 = 2x

Multiply both sides by 3: x + 75 = 6x

Subtract x from both sides: 75 = 5x 

Divide by 5 and get x = 15

First, we need to get everything on one side so that the equation equals zero.

2x² - 2x -2 = 1-x

We need to add x to the left, and then subtract 1.

2x² - 2x -2 +x - 1 = 0

2x² - x - 3 = 0

Now we need to factor the binomial. In order to do this, we need to multiply the outer two coefficients, which will give us 2(-3) = -6. We need to find two numbers that will mutiply to give us -6. We also need these two numers to equal -1 when we add them, because -1 is the coefficient of the x term.

If we use +2 and -3, then these two numbers will multiply to give us -6 and add to give us -1. Now we can rewrite the equation as follows:

2x² - x - 3 = 2x² + 2x - 3x - 3 = 0

2x² + 2x - 3x - 3 = 0

Now we can group the first two terms and the last two terms. We can then factor the first two terms and the last two terms.

2x(x+1) -3(x+1) = 0

(2x-3)(x+1) = 0

This means that either 2x - 3 = 0, or x + 1 = 0. So the values of x that solve the equation are 3/2 and -1.

The question asks us for the sum of the solutions, so we must add 3/2 and -1, which would give us 1/2. 

If we set one variable to the other we would get y = (2x – 7)/3 or x = (3y + 7)/2, but we aren't given any clues to what the values of x and y are and we can assume they could be any number. If x = 7/2, then y = 0. If y = -7/3, then x = 0. Let's try some other numbers. If y = –10, then x = –37/2. So for the first two examples, x is greater than y. In the last example, y is greater than x. We need more information to determine whether x or y is greater.  The correct answer is not enough information given.

When taking the absolute value we realize that both absolute value operations yield 8, which gives us a difference of 0.

You set up the equation 5x – 23 = 3x + 3, then solve for x, giving you 13.

First, solve for the values of x by factoring.

or

Then, multiply the solutions to obtain the product.

Collecting terms leaves 

And dividing by  yields

or

If you plug in the outer limits of the given ranges, (–1, ½) is the only combination that fits within the given equation. It is important to remember that "<" means “less than,” and "≤" means “less than or equal.” For example, if you answered (–2,2), plugging in 2 would make the the expression equal 8, which is greater than 3.5. And plugging in –2 for x would make the expression equal –4, which is less than –3, not greater. However, plugging in the correct answer (–1, ½) gives you –1 as your lower limit and 3.5 as your upper limit, which satisfies the equation. Both limits of the data set must satisfy the equation.