Wayground 23: Solutions

Multiple Choice

Which of the following scenarios represents an equation with: No Solutions?

• Variables cancel out, resulting in a false statement (e.g., 3 = 12)

• A single value makes the equation true (e.g., 3 = 3)

• Variables cancel out, resulting in a true statement (e.g., 2x+1 = 2x+1)

• The equation has multiple answers

Open Ended

Why is it important to understand the number of solutions an equation can have when solving algebraic problems?

Multiple Choice

Which of the following is NOT a step in solving linear equations as described in the lesson?

• Combine like terms

• Move variable terms to one side

• Multiply both sides by zero

• Divide to isolate x

Multiple Select

(Read the last slide):

What is the STEP 2 to solve: 3(4x + 2) = 20x - 9x + 2???

• Subtract 11x from both sides. . .

• Add 11x -- then divide. . .

• Distribute (multiply or divide). . .

• Find the variables. . .

Multiple Choice

What is the result when you subtract 8x from both sides in the equation 4(2x + 1) = 8x + 10?

• 4 = 10

• x = 2

• x = 5

• 8x = 8x

Fill in the Blanks

A linear equation with the same variable terms and same constant terms on both sides will have

solutions.

Hint: the word is on the last slide.

Another hint: It is no solutions, one solution, or infinite solutions.

Multiple Choice

What is the result when you solve the equation 4(2x - 8) = 8(x - 4)?

• No solution

• One solution

• Infinite many solutions

• x = 0

Open Ended

Explain how you can determine whether a linear equation has one solution, no solution, or infinitely many solutions based on its simplified form.

Fill in the Blanks

Fill in the blank: The equation 2(5x - 3) = 10x - 6 has

many solutions.

Is it none, one, or infinite?

Multiple Choice

Which of the following statements best describes an equation with infinite solutions?

• The variables cancel out and the resulting statement is true for all values.

• The variables cancel out and the resulting statement is false.

• There is only one value that makes the equation true.

• The equation has no variables.

Open Ended

Reflecting on today's lesson about equations with different numbers of solutions, what is one thing you still DO NOT understand or struggle with?