Translating Two and Multi-Step Inequalities

Solving Multi-Step

Inequalities

2.4 Day 2

Learning Target

Student will be able to…

●Solve multi-step inequalities.

●Use multi-step inequalities to solve real-life problems.

Multiple Choice

Solve: $$3f+9<21$$

• $$f<4$$

• $$f>4$$

• $$f\le4$$

• $$f\ge4$$

Multiple Choice

Solve: $$12\ge60-6x$$

• $$x<8$$

• $$x>8$$

• $$x\le8$$

• $$x\ge8$$

Multiple Choice

Solve: $$-5\le11-4p$$

• $$p<4$$

• $$p>4$$

• $$p\le4$$

• $$p\ge4$$

Multiple Choice

Solve: $$-3\left(x+2\right)\le-21$$

• $$x<5$$

• $$x>5$$

• $$x\le5$$

• $$x\ge5$$

Example 1: Solve and Graph

a)

6x-5 < 2x + 11

b) 5x - 12 ≤ 3x - 4

c) 3(2a - 1) ≥ 10a - 11

d)

Example 2: Inequalities with Special Solutions

a)

2(5c-7) ≥ 10(c-3)

b) -4(3n-1)>-12n+5.2

Example 3: Real-Life Applications

A school is taking a field trip with 195 students and 10 adults. Each bus can hold at most
40 students. We need to determine the smallest number of buses needed for the trip.

(a) Let n be the number of buses taken on the trip. Write and solve an inequality that

models this problem based on n.

(b)

Graph the solution on the number line

Math Response

$$3a-2\left(6a-4\right)>4-\left(4a+6\right)$$

Type answer here

Correct Answer: a<2

Deg^°

Rad