Solving Linear Inequalities in One Variable

Some Examples

Example 1:

Solve -8x − 2 ≥ -5x + 7

1) Add opps:
Complete the step:	(-2−7) ≥ (- 5+8)x	Now (-2−7) = -9 and (- 5+8) = 3
Then	- 9 ≥ 3x	3 is the coefficient of x
2) Multiply recip:		Since
Equivalent Property	- 3 ≥ x or x ≤ -3
3) Check:		Note that - 8 · - 3 = 24 and - 5 · - 3 = 15 x = - 3 is correct.

Since - 4 < - 3 choose x = - 4 as a replacement value for x and check.

Check (ineq):

Simplify.

x < -3 is correct

Any problems that have parentheses and/or fractions should be simplified first so that all constants are integers. Once they are simplified then follow the 3-steps shown. Check all of your answers

Example 2:

Solve the given inequality and graph the solution:

1) Write the equation:

2) Multiply by LCM = 6

3) Add Opps. See that 11 > 7, keep y there.

4 is coefficient of y

4) Multiply recip Note, y "on greater end"

5) Check (equals):

Choose y = 4 as replacement:

Check (ineq.):