1. Solving Multi Step Inequalities (3-4)

2. Algebra I Honors Guided Notes
9/12/14
Solving Multi Step Inequalities
*Solve just like you would a multistep equation*
-Use inverse operations to get the variable by itself
on one side of the inequality sign
Example 1 ) t ˃ 21 *subtract 9 from both sides
4t ˃ 12 *divide both sides by 4
4𝑡 4 ˃
t ˃ 3 *this means ALL numbers that
are greater than 3 would satisfy
this inequality
Check it:
9 + 4(4) ˃ 21
˃ 21
25 ˃ 21 true

3. You try:
-6a – 7 ≤ ˃ 0.8x +30
Example 2) 3(t + 1) – 4t ≥ -5 *distribute the 3
3t + 3 – 4t ≥ -5 *combine like terms
-1t + 3 ≥ -5 *subtract 3 from both sides
-1t ≥ -8 *divide both sides by -1
−1𝑡 −1 ≥ −8 −1
t ≤ 8 *So all numbers LESS THAN 8 will
satisfy this equation.
STOP!!!! Don’t forget. When you multiply or divide by a negative you HAVE to reverse the negative sign!!
You try: 15 ≤ 5 – 2(4m + 7)

4. Example 3) 6n – 1 ˃ 3n + 8 *combine like terms with
-3n n Inverse operations
3n – 1 ˃ 8
3n ˃ 9
3𝑛 3 ˃ 9 3
n ˃ 3 *so ALL numbers greater than 3
would satisfy the inequality
You try:
6z – 15 ˂ 4z x – 5 ≤ 3(6x – 2)

5. Example 4) 10 – 8a ≥ 2(5 – 4a) *Distribute the 2
10 ≥ * It is the SAME on both sides
*Since this is ALWAYS true, the solution to this inequality is all real numbers.
Example 5) 6m – 5 ˃ 7m + 7 – m *combine like terms
6m – 5 ˃ 6m + 7
-6m m
-5 ˃ 7
*This inequality is NEVER true so there is NO Solution
You try: n ≤ 5n – x ≥ 7x + 2 – x