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

### Solving Systems of Linear Inequalities Algebraically

x + 2 < 6 and x – 3 > – 1

### Solving System of Linear Inequalities Graphically

More Lessons for Algebra

Math Worksheets

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: *

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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