Solving algebraic equations

Multiple Choice

Which of the following is a key step in solving two-step equations?

• Applying inverse operations

• Guessing the value of the variable

• Multiplying both sides by zero

• Ignoring the variable

Open Ended

Why is it important to be able to solve algebraic equations in real-life situations?

Multiple Choice

Which of the following best describes an inverse operation?

• An operation that reverses the effect of another

• A symbol that represents an unknown value

• A mathematical statement showing two expressions are equal

• A number that does not change

Multiple Choice

Which of the following is a key step in solving two-step equations?

• Applying inverse operations

• Guessing the value of the variable

• Multiplying both sides by zero

• Ignoring variables on both sides

Open Ended

Why is it important to check solutions for accuracy when solving algebraic equations?

Multiple Choice

Which of the following equations is solved by dividing both sides by a number?

• x + 5 = 12

• x - 3 = 8

• 4x = 20

• x ÷ 6 = 2

Open Ended

Explain how inverse operations are used to solve one-step equations.

Multiple Choice

Solve:
-4x = 24

• 20
• -20
• 6
• -6

Multiple Choice

Solve
x/6 = 5

• 30
• 5/6
• 36
• 9

Multiple Choice

Solve -7/8 = m - 3/8.

• -5/4
• 1/2
• -1/2
• 5/4

Multiple Select

Which of the following statements are true about two-step equations?

• They require two inverse operations to isolate the variable

• They can always be solved in one step

• They never use addition or subtraction

• They require more than one operation to solve

Multiple Choice

Which of the following best describes an inverse operation?

• An operation that reverses the effect of another

• A symbol that represents an unknown value

• A mathematical statement showing two expressions are equal

• A number that does not change

Open Ended

Describe the steps needed to solve the equation 2x + 3 = 11.

Multiple Choice

How do you solve a one-step equation involving a variable?

• By using only one operation to isolate the variable

• By using two operations to isolate the variable

• By guessing the value of the variable

• By adding all numbers together

Multiple Choice

Which of the following is a key feature of multi-step equations as described in the slides?

• They always require only one operation to solve.

• They may involve distributing, combining like terms, and multiple operations.

• They never require combining like terms.

• They only have variables on one side.

Multiple Choice

Solve:
6(5x - 3) + 2 = 14

• 2
• .5
• -1
• 1

Multiple Choice

Solve:
6(5x - 3) + 2 = 14

• 2
• .5
• -1
• 1

Multiple Select

Select all the steps that are part of solving the equation 3(x + 2) - 4 = 11 as shown in the slides.

• Distribute 3 to (x + 2)

• Combine like terms

• Multiply both sides by 2

• Divide by 3

Open Ended

Explain the steps needed to solve a multi-step equation, using the example provided in the slides.

Multiple Choice

Which of the following equations requires distributing as the first step to solve?

• 5x - 2 = 13

• 2(x - 4) + 3 = 11

• 4x - 2x + 6 = 10

• 7 = 2x - 1

Open Ended

Explain the difference between one-step and two-step equations using examples from the slides.

Multiple Choice

In the equation 2x + 5 = x + 8, what is the value of x?

• x = 1

• x = 2

• x = 3

• x = 4

Multiple Choice

Which of the following is the correct solution for the equation 3x + 2 = 5x - 6?

• x = 4

• x = -4

• x = 2

• x = -2

Multiple Select

Which of the following are examples of one-step equations?

• x + 5 = 12

• x - 3 = 8

• 4x = 20

• 2x + 3 = 11

Multiple Choice

Solve: 

• 8
• 17/12
• 4/3
• 1/8

Multiple Select

Which strategies should you use when solving two-sided equations?

• Perform inverse operations

• Keep equations balanced

• Simplify each side before solving

• Guess and check

Open Ended

Explain why it is important to keep equations balanced when solving for a variable.

Open Ended

What are the steps to solve the equation 2x + 3 = 11?

Multiple Choice

Which of the following is a correct first step to solve the equation 5x - 2 = 13?

• Add 2 to both sides

• Divide both sides by 5

• Subtract 5 from both sides

• Multiply both sides by 2

Multiple Choice

Which operations are typically involved in solving multi-step equations?

• Distributing, combining like terms, and multiple operations

• Only addition and subtraction

• Only multiplication and division

• Factoring and graphing

Open Ended

Explain the difference between two-step equations and multi-step equations. Provide an example of each.

Open Ended

Why is it important to get all variables on one side and constants on the other when solving two-sided equations?

Multiple Select

Select all the correct steps in solving the equation 2x + 5 = x + 8.

• Subtract x from both sides

• Add 5 to both sides

• Subtract 5 from both sides

• Divide both sides by 2

Multiple Choice

Which of the following is the correct first step to solve the equation 3x + 2 = 5x - 6?

• Subtract 2 from both sides

• Add 6 to both sides

• Subtract 3x from both sides

• Add 5x to both sides

Multiple Choice

Which of the following is NOT a learning objective for solving algebraic equations as described in the lesson?

• Understand and solve one-step equations.

• Apply inverse operations in two-step and multi-step equations.

• Memorize the quadratic formula.

• Check solutions for accuracy.

Open Ended

Explain why it is important to keep equations balanced when solving for a variable. Use examples from the strategies recap.

Multiple Choice

Solve the equation below:

• k = 152

• k = 176

• k = 5

• k = 27

Multiple Select

Which of the following steps are necessary to solve the equation 2(x - 1) + 3 = x + 5?

• Distribute the 2 to both terms inside the parentheses

• Add 1 to both sides first

• Simplify both sides before isolating x

• Subtract x from both sides

Multiple Choice

Which equation has x = 5 as the answer?

• x + 15 = 10

• 2x = 5

• 2x = 10

• 2x - 3 = 15

Multiple Choice

-4x + 1 = 21

• x=120
• x=5
• x=30
• x=-5

Open Ended

How confident do you feel about solving equations with variables on both sides after this lesson? What would you like to review or practice more?

Multiple Choice

3x - 5 = -26

• x=-21

• x=21

• x=-7

• x=61

Multiple Choice

Which of the following is NOT a learning objective for solving algebraic equations as listed in the lesson?

• Understand and solve one-step equations.

• Apply inverse operations in two-step and multi-step equations.

• Memorize all possible algebraic equations.

• Check solutions for accuracy.

Multiple Choice

Solve: 3(x-4) = -3

• 3
• -3
• 5
• -5

Multiple Choice

Janet wants to rent a U-Haul to move her mother. She spends $225 for the move. The U-Haul costs $45 up front and $1.50 a mile. What equation would you use to solve the number of miles her mother moved?

• 225 = 45x + 1.5

• 45 + 1.5x = 225

• 45x + 1.5x = 225

• 225 = 45(1.5) + 1.5x

Open Ended

How confident do you feel about solving equations with variables on both sides after this lesson? What would you like to practice more?

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.

Multiple Choice

Solve:
2(2t - 3) = 6(t + 2)

• t=9
• t=4
• t=-9
• t=-3

Multiple Choice

A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear.  They sell the teddy bears for $12 a piece.  Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?

• 1500 + 8t = 12
• 12 + 8t = 1500
• 1500 + 8t = 12t
• 8t = 12t + 1500

Multiple Choice

What is the first step in solving the equation 2a - 4(a - 5) = 10

• Add 4 to both sides
• Add the 2a and a 
• Distribute 4 to a and -5
• Distribute -4 to a and -5

Multiple Choice

8v - 4(v + 8) = 8

• 2
• 10
• 4
• -4 

Multiple Choice

2x - 3 + 4x = 27

• 12
• 4
• 5
• 15

Multiple Choice

2x + 3(5x - 7) = 47

(enter the number only)

• 1

• 2

• 3

• 4

Multiple Choice

x + 9 = 23

• 32

• 14

• 12

• 33

Multiple Choice

3n = 39

• 117

• 36

• 12

• 13

Multiple Choice

What is the first step in solving this equation:
5x + 7 = 12

• Divide by 5
• Subtract 5
• Multiply by 7
• Subtract 7

Multiple Choice

Solve:
3x + 7 = -8

• 5
• -5
• -12
• -18

Multiple Choice

x - 5.5 = 10.5

• x = 15
• x = 14
• x = 16
• x = 15.5

Multiple Choice

What is the first step to complete when solving this equation?
10 - 3y = 4

• Add 10
• Subtract 10
• Add 3
• Divide by -3

Multiple Choice

Solve for g: 
2g - 3 + 4g = 27

• g = 12
• g = 4
• g = 5
• g = 15

Multiple Choice

Solve:

-8 + 5x - 2 = 20

• 6

• -6

• 2

• -2