Multi Step Inequalities

​Multi-Step Inequalities

Multiple Choice

x + 5 > 7

• x > -2
• x > 2
• x > 12
• x > -12

Multiple Choice

Which inequality is represented by the  following graph

• x > 9
• x < 9
• x ≥ 9
• x ≤ 9

Remember Inequality Symbols

< ≤ Points to the Left - Less

​

> ≥ Points to the Right - gReater

Steps

• Find the number where you have your circle

• Is the circle

  Ο empty (< or >)

  ⊗ filled (≤ or ≥)

• Points Left means Less (< or ≤)

• Points Right means gReater (> or ≥)

​subtract 7 from both sides

​add 8 to both sides

​subtract 6 from both sides

​add 5 to both sides

divide both sides by 6

multiply both sides by 4

multiply both sides by -3

divide both sides by -7

Two-step inequalities

• The symbol is less or equal

• Undo subtraction by adding 5 to both sides

• Undo multiplication by dividing by 3 on both sides

• Graph on the number line

• Circle is filled and arrow points to the left

Solve an inequality

• Symbol gReater or equal to (points to the Right)

• Undo subtraction by adding 3 to both sides

• Undo division by multiplying by 6 both sides

• Graph on the number line

• Circle is filled and arrow points to the right

Multiple Choice

What is the correct solution for

$$\frac{a}{6}-3\ge-2$$  

• a < 6

• a > 6

• a ≤ 6

• a ≥ 6

Multiple Choice

$$4\left(8a-6\right)+a<108$$  

what is your first step?

• add 6 to both sides

• distribute 4 to the quantity (8a-6)

• add a to both sides

• combine 8a-6 to get 2

Multiple Choice

$$4\left(8a-6\right)+a<108$$  

what is your final answer?

• a<132

• a>11

• a<33

• a<4

​Inequalities with variables on BOTH SIDES

​

• Move all variable terms to the LEFT side of the inequality and all constant terms to the RIGHT side

  ​

• (Mueve todos los términos variables a la izquierda de la desigualdad y todas las constantes a la derecha)​

You should know the parts of an expression!!

Multiple Choice

4x - 3 < -1x + 12

• x > 3
• x < 3
• x < 5
• x > 5

Multiple Choice

-2x + 2 > 3x - 8 

• x > -9
• x > 2
• x < -9 
• x < 2

Multiple Choice

3(x - 3) ≤ 2(x + 2)

• x ≤ -5
• x ≥ 5
• x ≥ 13
• x ≤ 13

Multiple Choice

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she can spend no more than $35 in all.

• .50x + 20 ≥ 35

• .50x < 35

• .50x + 20 ≤ 35

• .50x - 20 = 35

Multiple Choice

A limo driver needs to make more than $450 in one day.  He charges a rental fee of $375 and $0.85 per mile.  What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450
• 0.85x + 375 < 450
• 0.85 + 375x > 450
• 0.85 + 375x < 450

​4 Steps to Solve Multi-Step Inequalities

​

1. Use the distributive property if possible

   (Usa la propiedad distributiva si es posible)

2. Combine like terms

   (Combine términos semejantes)

3. Move variable terms to the left and constants to the right.

   (Mueve los términos variables a la izquierda y las constantes a la derecha de la desigualidad)

4. Solve the simplified equation using inverse operations.

   (Resuelve la ecuacion simplificada usando operactiones inversas)​

Thank you for your attention!

I am glad we are on this adventure together!​