Equations and Inequalities Test Review

Equations and Inequalities Test Review

By Alexandra KnightdaleHS

How do we solve equations?

How to solve multistep equations

1. Simplify each side.

2. Eliminate the variable from the right side.

3. Eliminate the constant term from the left side.

4. Divide each side by the coefficient.​

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​Examples on Solving Equations

Multiple Choice

An Equation is...

• A problem that contains at least one operation; no equal sign

• A mathematical sentence showing two expressions are equal

• The solution for a variable

• The value that results in a true sentence

Multiple Choice

A solution is...

• The value that results in a true sentence

• A mathematical sentence showing two expressions are equal

• Numbers expressed using exponents

• The value for the variable in an equation

Multiple Choice

Inverse Operations are operations which undo each other

• True

• False

Multiple Choice

Solve for x

$$4+\frac{x}{2}=-3$$  

• 14

• -14

• 4

• -2

Multiple Choice

What is the first step to solve this equation?

$$-11-3x=44$$  

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides

How do we solve literal equations?

Solve Literal Equations

• A literal equation is an equation with more than one variable.

• To solve a literal equation means to isolate the indicated variable. We can use inverse operations to solve the variable.​

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Multiple Choice

-2 = 4r + s solve for s.

• s = -2 + 4r

• s = 2 - 4r

• s = -2 - 4r

• s = 2 + 4r

Multiple Choice

$$-3x\ +2c\ =\ 3\ \ \ \ \ \ \ \ solve\ for\ x$$  

• $$x=\frac{3-2c}{-3}$$  

• $$x\ =\ 6+2c$$  

• $$x\ =\ 6-2c$$  

• $$x\ =\ \frac{3+2c}{3}$$  

Multiple Choice

Solve for p $$A=\frac{1}{2}pa$$  

• $$A-\frac{1}{2}a\ =\ p$$

• $$\frac{2A}{a}=p$$

• $$\frac{A}{2a}=p$$

• $$2A-a\ =\ p$$

Multiple Choice

Solve for p $$SA=hp+2B$$  

• $$\frac{SA-2B}{h}=p$$

• $$\frac{SA}{h}-2B=p$$

• $$\frac{SA-h}{2B}=p$$

• $$SA-2B-h=p$$

Inequalities

What is an inequality?

• Used to model a situation that has a range of answers instead of just a single answer.​

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Inequalities

How do we solve inequalities?

1. Add or subtract to isolate the variable term.

2. Multiply or divide to solve for the variable. If multiplying or dividing by a negative number, then reverse the inequality symbol.​

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Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 
• <, >
• ≤, <
• ≥, >

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Choice

-3 − 6(4x + 6) > -111

• x > 3
• x < 3
• x < -3
• x > -3

Multiple Choice

When do you flip the inequality symbol?

• if your answer is negative
• when you multiply or divide by a negative number
• you never flip it
• when you add or subtract by a negative number

Multiple Choice

Write an inequality:
Twenty-two more than four times a number is less than 82.

• 22 + 4n ≤ 82
• 22 + 4n > 82
• 82 + 22n ≥ 4
• 22 + 4n < 82

Multiple Choice

6. Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell? 

• x/5.50 ≥ 5225
• 5.50x ≥ 5225
• x + 5.50 ≤ 5225 
• x - 5.50 ≤ 5225

Multiple Choice

Jo needs to collect at least 1,000 signatures for a petition. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which inequality represents this situation?

• $$520x+6\le1000$$  

• $$520+6x\ge1000$$  

• $$520x+6\ge1000$$  

• $$520+6x\le1000$$  

Multiple Choice

Jo needs to collect at least 1,000 signatures for a petition. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which solution represents how many signatures Jo needs each week?

• $$x\ge80$$

• $$x\ge2$$

• $$x\le80$$

• $$x\le2$$

Multiple Choice

What equation can express this picture?

• -6+8x=50

• 50x=6x+2

• 6x-2=50

• 6x+8=50

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

$$-\frac{1}{8}y\le34$$  Solve for y 

• $$y\le-136$$  

• $$y\ge-425$$  

• $$y\ge-272$$