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We can solve systems of linear inequalities either algebraically or graphically.

When solving systems of linear inequalities (or simultaneous inequalities):

**Step 1**: Solve each inequality separately

**Step 2:** Find the common values between the two inequalities. (Use a number line if necessary)

*Example: *

Solve the following simultaneous inequalities and represent your solution set on the number line.

x + 2 < 6 and x – 3 > – 1

*Solution:*

x + 2 < 6

x < 6 – 2

x < 4

x – 3 > – 1

x > – 1 + 3

x > 2

Common values: 2 < x < 4

*Example:*

Find the integer values of *x* satisfying the simultaneous inequality:

6 < 2 – 3*x* < 14

**Solution:**

Write 6 < 2 – 3*x* < 14 as two separate inequalities and solve them separately.

6 < 2 – 3*x*

3*x* < 2 – 6

3*x* < – 4

* x* <

2 – 3*x* < 14

– 3*x* < 14 – 2

– 3*x* < 12

3*x* > –12

* x* > – 4

Common values: – 4 < *x* <

The integer values of *x* are –3 and –2

We can also solve systems of linear inequalities graphically. The following videos show some examples of solving systems of linear inequalities graphically

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