Guided Practice

The symbol ≤ means "less than or equal to," and ≥ means "greater than or equal to."

If we suppose that x ≥ 0, we can model the inequality 2x + 4 < 8 this way:

We can see from the diagram that x can be any value between 0 and 2. Try different values of x to make the inequality true or false.

The expression x < 1 means x is than 1.

The expression x > 1 means x is than 1.

Suppose that p > 5. Write T next to each true statement, F next to each false statement, and U next to each statement whose truth is unknown. (The symbol ≠ means "is not equal to.")

p ≠ 5

p = 6

p = 5

Suppose that w < 4. Write T next to each true statement, F next to each false statement, and U next to each statement whose truth is unknown. (The symbol ≠ means "is not equal to.")

w < 3

w ≠ 2

w < 5

Suppose that x < 10. Write T next to each true statement, F next to each false statement, and U next to each statement whose truth is unknown.

10 > x

x = 10

11 = x

Suppose that 22 < q. Write T next to each true statement, F next to each false statement, and U next to each statement whose truth is unknown.

q > 22

q = 22.01

q < q

Suppose that y > 4 – 1. Write T next to each true statement, F next to each false statement, and U next to each statement whose truth is unknown. (The symbol ≠ means "is not equal to.")

4 < y

y ≠ 3

y > 2

Enter different values for x to make the inequality 2x + 4 < 8 true. Decimals and integers only.

2() + 4 < 8

2() + 4 < 8

2() + 4 < 8

Enter different values for g to make the inequality 3g – 3 > 6 true. Decimals and integers only.

3() – 3 > 6

3() – 3 > 6

3() – 3 > 6

Enter different values for s to make the inequality s + 5 < 10 true. Decimals and integers only.

+ 5 < 10

+ 5 < 10

+ 5 < 10

Enter different values for n to make the inequality 0.5n > 3 true. Decimals and integers only.

0.5() > 3

0.5() > 3

0.5() > 3

Enter different values for m to make the inequality m + 0 > 1 true. Decimals and integers only.

+ 0 > 1

+ 0 > 1

+ 0 > 1

Enter different values for y to make the inequality 2y – (–10) < –5 true. Decimals and integers only.

2() – (–10) < –5

2() – (–10) < –5

2() – (–10) < –5

Think about the inequality x < –1. If we multiply both sides by –5, we get –5x < 5. But if we substitute different numbers for x, we get false statements.

–5(–2) < 5 ← False.

–5(–3) < 5 ← False.

Whenever we multiply or divide both sides of an inequality by a negative number, everything flips, so we have to flip the inequality sign too:

x < –1, so –5x > 5

Complete each inequality statement using > or <.

–4 –1

(–1)(–4) (–1)(–1)

Complete each inequality statement using > or <.

3 2

(–2)(3) (–2)(2)

Complete each inequality statement using > or <. Draw a number line to show your work.

6 –2

(–1)(6) (–1)(–2)

Complete each inequality statement using > or <. Draw a number line to show your work.

–5 5

(–4)(–5) (–4)(5)

Complete each inequality statement using > or <. Draw a number line to show your work.

3 8

(5)(3) (5)(8)

Complete each inequality statement using > or <. Draw a number line to show your work.

1/23/2

(–4/5)(1/2)(–4/5)(3/2)

Complete each inequality statement using > or <. Draw a number line to show your work.

4 12

4 ÷ (–1) 12 ÷ (–1)

Complete each inequality statement using > or <. Draw a number line to show your work.

1 –7

1 ÷ (–8) –7 ÷ (–8)

Complete each inequality statement using > or <. Draw a number line to show your work.

–5 –6

–5 ÷ (4) –6 ÷ (4)

Complete each inequality statement using > or <. Draw a number line to show your work.

3/8 –1/2

–(–3/8) ÷ (–1/2)(–1/2) ÷ (–1/2)

Complete each inequality statement using > or <. Draw a number line to show your work.

–2 0

(–1)(–2) (–1)(0)

Complete each inequality statement using > or <. Draw a number line to show your work.

0 4.5

(–3.2)(0) (–3.2)(4.5)

To write an inequality for a word problem, it helps to start with an equation. For example, Ben's mom is 30 years older than he is. How old will Ben be when his mom is older than 50?

Start with an equation. How old will Ben be when his mom is exactly 50?

b + 30 = 50 ← If Ben's mom is exactly 50.

b = 20 ← Ben is exactly 20.

Since Ben's mom's age can be represented as b + 30, his mom being older than 50 can be written as b + 30 > 50. So, rewrite:

b + 30 > 50 ← If Ben's mom is older than 50.

b > 20 ← Ben is older than 20.

Complete the inequality to represent Ben's mom's age if she is younger than 40. Then, complete the sentence to show Ben's age.

b + 30

If Ben's mom is younger than 40, Ben is younger than .

Tisha bought 4 notebooks and spent less than 20 dollars.

Complete the inequality to represent the cost of 4 notebooks. Then, complete the sentence to show the cost of one notebook.

4 • n

One notebook cost less than $.

Erin withdrew $40 from her savings, which still left her with more than $100 in the account.

Complete the inequality to represent the amount that was in Erin's savings account after her withdrawal. Then, complete the sentence to show the amount before the withdrawal.

s – 40

There was more than $ in the account.

Three friends split up a road trip equally. The first day, each friend drove for more than 250 miles.

Complete the inequality to represent the total number of miles each friend drove. Then, complete the sentence to show the total number of miles they drove together the first day.

m ÷ 3

Together, the friends drove more than miles the first day.

x

x =

For each inequality modeled on the left, x is greater than or equal to 0.

Move the slider to show the solutions for x, enter the inequality, then press check.

Once you have solved all 10 inequalities on the diagram, you can click the checkmark below.

For each equation modeled on the left, x is greater than or equal to 0.

Move the slider to show the solution for x, complete the equation, then press check.

Once you have solved all 10 equations on the diagram, you can click the checkmark below.

Solve the inequality –x < 1.

x >