When we solve algebraic inequalities, our aim is to end up with one letter on one side of the inequality sign and one number on the other. This is the solution.

Just as in solving equations, we do this by using inverse operations to undo things that get in the way, but remember that we must **do the same thing to both sides.**

**If you reverse an inequality, remember to reverse the sign.**

**5 < 8**

**8 > 5**

**Example**

5b + 3 > 23

**Answer**

Subtract 3 from both sides:

5b + 3 - 3 > 23 - 3

Simplify:

5b > 20

Divide both sides by 5:

5b ÷ 5 > 20 ÷ 5

Simplify:

**b > 4**

**Example**

b/5 - 3 ≤ 17

**Answer**

Add 3 to both sides:

b/5 - 3 + 3 ≤ 17 + 3

Simplify:

b/5 ≤ 20

Multiply both sides by 5:

b ÷ 5 x 5 ≤ 20 x 5

Simplify:

**b ≤ 100**

**Example**

Solve for a

5 - a ≥ 10

**Answer**

Add a to both sides:

5 - a + a ≥ 10 + a

Simplify:

5 ≥ 10 + a

Subtract 10 from both sides:

5 -10 ≥ 10 - 10 + a

Simplify:

-5 ≥ a

**REVERSE **and be careful to** change the SIGN DIRECTION:**

**a ****≤ **-5

Does that all make sense?

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