Over Lesson 5–3

A. AB. BC. CD. D

Write an inequality for the sentence. A number decreased by 7 is at most 9.

Write an inequality for the sentence. There are more than 500 students (s) at Candlewood Middle School.

What inequality represents the graph?

You have already used the Properties of Equality to solve equations.(Lessons 4–3 and 4–4)

• Solve inequalities with Addition and Subtraction.

• Solve inequalities with Multiplication and Division (tomorrow).

• To solve inequalities, first pretend they are equal. This will allow you to use your previously learned algebra skills.

• After you have completed the problem as if it were equal, we graph the critical point (what it is “equal to”) and make sure we make either an open circle or closed circle (depending on the inequality)

• Test values using the original inequality and write the inequality the graph represents.

So you want to solve inequalities? Maybe you’re crazy!…lol

Solve an Inequality

Solve y + 5 > 11. y + 5 > 11

Write the inequality. y + 5 = 11 Pretend it is equal - 5 - 5 Subtract 5 from both

sides. y = 6 This is our critical point (graph it)

0 6

Answer: The solution is y > 6.

Test values to the left and right of 6. Plug in 0 into theoriginal inequality. Does it work? Try 7 into the originalinequality. Does it work? Now shade!

Solve an Inequality

Solve y - 3 ≤ -2. y - 3 ≤ -2Write the

inequality. y - 3 = -2 Pretend it is equal +3 +3 Add 3 to both sides. y = 1 This is our critical point (graph it)

0 1

Answer: The solution is y ≤ 1.

Test values to the left and right of 1. Plug in 0 into theoriginal inequality. Does it work? Try 3 into the originalinequality. Does it work? Now shade!

Solve an Inequality

Solve y - 5 > -9. y - 5 > -9Write the

inequality. y - 5 = -9 Pretend it is equal +5 +5 Add 5 from both

sides. y = -4 This is our critical point (graph it)

-4 0

Answer: The solution is y > -4.

Test values to the left and right of -4. Plug in -5 into theoriginal inequality. Does it work? Try 0 into the originalinequality. Does it work? Now shade!

Solve an Inequality

Solve y + 6 ≥ 6. y + 6 ≥ 6 Write the inequality. y + 6 = 6 Pretend it is equal - 6 - 6 Subtract 6 from both

sides. y = 0 This is our critical point (graph it)

0

Answer: The solution is y ≥ 0.

Test values to the left and right of 0. Plug in -1 into theoriginal inequality. Does it work? Try 2 into the originalinequality. Does it work? Now shade!

A. AB. BC. CD. D

A. x < 22

B. x < 4

C. x < –4

D. x > 4

Solve x + 9 < 13.

A. AB. BC. CD. D

Solve Graph the solution on a number line.

A.

B.

C.

D.

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Let’s do some practice at our seats with this worksheet I am about to handout!