To solve an equality that has addition, simply treat it as an equation. Remember, the only time you have to do something to the inquality is when you are multiplying or dividing by a negative number.

Subrtract 4 from each side. Thus,

Simplifying an inequality like this is very simple. You merely need to treat it like an equation—just don't forget to keep the inequality sign.

First, subtract from both sides:

Then, divide by :

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, solve the inequality :

Since we are dealing with absolute value, must also be true; therefore:

First separate the inequality into two equations.

Solve the first inequality.

Solve the second inequality.

Thus, or .

Absolute value is the distance from the origin and is always positive.

So we need to solve and which becomes a bounded solution.

Adding 3 to both sides of the inequality gives and or in simplified form

First, we want to group all of our like terms. I will move all of my integers to the left side of the inequality.

Since we are not dividing by a negative sign, we do not have to flip the inequality.

We must put all of the like terms together on either side of the inequality symbol. First, we need to subtract the to the right side and add to the left side to get all of the terms with to the right side of the inequality and all of the integers to the left side.

We solve for by dividing by .

That leaves us with , which is the same as . Remember, you only flip the direction of the inequality if you divide by a negative number!

3_w_/2 will become greater than 1 as soon as w is greater than two thirds. It will likewise become less than –1 as soon as w is less than negative two thirds. All the other options always return values between –1 and 1.

The first thing that we have to do is deal with the absolute value. We simply remove the absolute value by equating the left side with the positive and negative solution (of the right side). When we include the negative solution, we must flip the direction of the inequality. Shown explicitly:

Now, we simply solve the inequality by moving all of the integers to the right side, and we are left with: This reduces down to