Inequalities Part 2

Inequalities Part 2

What About Solving Inequalities?

•  $7>3$  Is true, so let's see what happens when we manipulate it.

•  $\left(7\right)+2>\left(3\right)+2$  

•             $9>5$  

• Adding a positive number to both sides doesn't have an affect on the inequality symbol.

•  $\left(7\right)+-2\ >\ \left(3\right)+-2$  

•                 $5\ >1$  

• Adding a negative number to both sides doesn't have an affect on the inequality symbol.

Multiple Choice

Solve the inequality.

30 + n ≥ 50

• n > 50

• n ≥ 80

• n < 30

• n ≥ 20

Multiple Choice

x + 5 > 7

• x > -2

• x > 2

• x > 12

• x > -12

Multiple Choice

-4 + y < -8

• y < 4
• y < -12
• y < -4
• y < 12

What About Solving Inequalities?

•  $7>3$  Is true, so let's see what happens when we manipulate it.

•  $\left(7\right)\left(2\right)>\left(3\right)\left(2\right)$  

•          $14>6$  

• Multiplying both sides by a positive doesn't have an effect on the inequality symbol.

•  $\frac{\left(7\right)}{2}>\frac{\left(3\right)}{2}$  

•  $2.5>1.5$  

• Dividing both sides by a positive doesn't have an effect on the inequality symbol.

Multiple Choice

Solve:
8m - 9 > 71

• m > 10
• m > 1
• m < 1
• m > -48

Multiple Choice

Solve the following inequality. Show your algebraic work!

• b > 6

• b < -4

• b > 1

• b < -12

Multiple Choice

Solve the inequality:

4x + 1 > 13

• x > 48

• x < 3

• x > 3.5

• x > 3

Multiple Choice

Solve the inequality.

 $2x+5>19$  

•  $x>7$  

•  $x<7$  

•  $x>12$  

•  $x<28$  

What About Solving Inequalities?

•  $7>3$  Is true, so let's see what happens when we manipulate it.

•  $\left(7\right)\left(-2\right)>\left(3\right)\left(-2\right)$  

•          $-14>-6\ \ IS\ NOT\ TRUE....$   $-14\ <-6\ \ \ But\ if\ you\ flip\ the\ inequality,\ it's\ true.$ 

•  $\frac{\left(7\right)}{-2}>\frac{\left(3\right)}{-2}$  

•  $-2.5>-1.5\ IS\ NOT\ TRUE$  

•  $-2.5\ <-1.5\ \ \ But\ if\ you\ flip\ the\ inequality,\ it's\ true.$  
  

• Multiplying or dividing both sides by a negative number reverses the inequality symbol.

Solving an Inequality with a Positive Coefficient

• The steps stay the same as when solving an equation

• Since no side was multiplied or divided by a negative, the symbol stays the same.

Solving an Inequality with a Negative Coefficient

• The steps stay the same as when solving an equation

• However, notice that at the step when they divided both sides by -3, the inequality symbol had to reverse to the opposite one

Multiple Choice

Do you need to flip the sign while solving this inequality?

3x ≥ 12

• Yes

• No

Multiple Choice

Do you need to flip the sign while solving this inequality?

-3x ≥ 12

• Yes

• No

Multiple Select

In which inequalities will the inequality symbol need to be reversed when solving? 

Hint: There are TWO correcet answers.

• $\frac{x}{9}\le-18$

• $-9x<-18$

• $-9x<18$

• $4x-6\le-12$

Multiple Choice

Solve the inequality:

22 < 6c + 4

• 11 > c

• 3 > c

• 11 < c

• 3 < c

Multiple Choice

Solve the inequality:

2 - 3x ≤ 20

• x ≥ -6

• x ≤ -6

• x ≤ -7

• x ≥ -7