   # SOLVING LINEAR INEQUALITIES - Friends University ... SOLVING LINEAR INEQUALITIES Solving a linear inequality

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• SOLVING LINEAR INEQUALITIES

Solving a linear inequality is just like solving a regular equality (or a regular equation). Let’s look at an example:

Solve for x:

4𝑥 − 3 > 2𝑥 − 2

We first start by combining our “like terms” or our “similar terms”. Let’s start by subtracting the 4x over to the right-hand side.

4𝑥 − 3 > 2𝑥 − 2  −4𝑥         − 4𝑥  −3 > −2𝑥 − 2 Now let’s move our ‐2 over from the right‐hand side. −3 > −2𝑥 − 2  +2           + 2  −1 > −2𝑥

We’re almost done. Now we have to divide both sides by -2. Since we’re dividing by a negative number, we MUST switch the way the inequality sign is pointing.

−1 > −2𝑥  −2    − 2    1 2 < 𝑥

Therefore, x is greater than ! ! .

• GRAPHING LINES

Graphing an equation is a simple process that can seem difficult at first. Let’s take a look at an example:

Graph the equation 𝑦 = 2𝑥 + 6.

First we need to look at our y-intercept or our “b” in the form y = mx + b. In our example, our y- intercept is 6. So we start by plotting our y-intercept on the y-axis (or the axis that goes up and down).

The next thing we need to do is find the next point. We do this by replacing x with 1 (because 1 is our next point) in our equation.

𝑦 = 2 1 + 6 = 8

So our next point on the graph is at (1 , 8) and connect them.

0  1  2  3  4  5  6  7

Series1

• We continue this process. The next graph will show you on the interval [0 , 6].

0  1  2  3  4  5  6  7

0  2  4  6  8  10  12  14  16  18  20

0  1  2  3  4  5  6  7

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