Solving Multi Step Inequalities (3-4)

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 ) 9 + 4t ˃ 21 *subtract 9 from both sides -9 -9 4t ˃ 12 *divide both sides by 4 4𝑡 4 ˃ 12 4 t ˃ 3 *this means ALL numbers that are greater than 3 would satisfy this inequality Check it: 9 + 4(4) ˃ 21 9 + 16 ˃ 21 25 ˃ 21 true

You try: -6a – 7 ≤ 17 50 ˃ 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 -3 -3 -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)

Example 3) 6n – 1 ˃ 3n + 8 *combine like terms with -3n -3n Inverse operations 3n – 1 ˃ 8 +1 +1 3n ˃ 9 3𝑛 3 ˃ 9 3 n ˃ 3 *so ALL numbers greater than 3 would satisfy the inequality You try: 6z – 15 ˂ 4z + 11 18x – 5 ≤ 3(6x – 2)  

Example 4) 10 – 8a ≥ 2(5 – 4a) *Distribute the 2 10 ≥ 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 -6m -5 ˃ 7 *This inequality is NEVER true so there is NO Solution You try: 9 + 5n ≤ 5n – 1 8 + 6x ≥ 7x + 2 – x