Begin by adding  to both sides, this will get the variable isolated:

Or...

Next, divide both sides by :

Notice that when you divide by a negative number, you need to flip the inequality sign!

Choice a is equivalent because we can say that technically we are multiplying two fractions together: (xy)/z and (5(x + y))/1.  We multiply the numerators together and the denominators together and end up with xy (5x + 5y)/z.  xy (5y + 5x)/z is also equivalent because it is only simplifying what is inside the parentheses and switching the order- the commutative property tells us this is still the same expression.  5x²y + 5xy²/z is equivalent as it is just a simplified version when the numerators are multiplied out.  Choice 5x² + y²/z is not equivalent because it does not account for all the variables that were in the given expression and it does not use FOIL correctly.

We simplify this inequality similarly to how we would simplify an equation

Thus 

In order to find the solution set, we solve  as we would an equation:

Therefore, the solution set is any value of .

For the most part, you can treat inequalities just like equations. (It is not exact, as you will see below.) Thus, start by isolating your variables.  Subtract  from both sides:

Next, subtract  from both sides:

Finally—here you need to be careful—divide by . When you divide or multiply by a negative value in inequalities, you need to flip the inequality sign. 

Thus, you get:

When solving an inequality in which you have to mulitiply or divide by a negative number, you must "flip" the direction of the inequality. Other than that, solve it nomrally.

Thus the first and only step we have is to divide by  and since that number is negative, we "flip" the inequality.

Yielding:

To solve, simply solve as though it is an equation.

The goal is to isolate the variable on one side with all other constants on the other side. Perform the opposite operation to manipulate the inequality.

Only when dividing or multiplying by a negative number, will you have to flip the inequality sign.

To solve, simply treat it as an equation.

This means you want to isolate the variable on one side and move all other constants to the other side through opposite operation manipulation.

Remember, you only flip the inequality sign if you multiply or divide by a negative number.

Thus,

First, simplify the equation so the absolute value is all that remains on the left side of the equation:

|2x – 25| = 10

Now create two equalities, one for 10 and one for –10.

2x – 25 = 10        and        2x – 25 = –10

2x = 35               and        2x = 15

x = 17.5              and          x = 7.5

The two solutions are 7.5 and 17.5.  17.5 + 7.5 = 25

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