Four Steps to Solve Absolute Value Equations

Maria, a mathematician, explains how to solve absolute value equations in four steps. First, isolate the absolute value on one side of the equation. Next, create two separate equations by removing the absolute value bars. Then, solve each equation using inverse operations. Finally, check both solutions to ensure they satisfy the original equation. Maria demonstrates these steps with an example, ensuring clarity and understanding.

What is the first step in solving an absolute value equation?

• Combine like terms

• Add 3 to both sides

• Isolate the absolute value expression

• Multiply both sides by 2

What operation is used to isolate the absolute value expression in the equation |M - 3| + 2 = 6?

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply both sides by 2

• Divide both sides by 2

After isolating the absolute value expression, what is the next step?

• Square both sides of the equation

• Add the same number to both sides

• Create two separate equations

• Combine like terms

What are the two equations formed from |M - 3| = 4?

• M - 3 = 4 and M - 3 = -4

• M + 3 = 4 and M + 3 = -4

• M - 3 = 4 and M + 3 = 4

• M - 3 = 4 and M = 4

What is the third step in solving an absolute value equation?

• Combine like terms

• Solve each equation using inverse operations

• Check the solutions

• Multiply both sides by 2

What is the solution to the equation M - 3 = 4?

• M = 7

• M = -7

• M = 1

• M = -1

What is the solution to the equation M - 3 = -4?

• M = 7

• M = 1

• M = -1

• M = -7

What is the final step in solving an absolute value equation?

• Add the same number to both sides

• Combine like terms

• Check both solutions

• Multiply both sides by 2

What should you do to check the solution M = 7 in the original equation?

• Add 7 to both sides

• Substitute -7 for M and simplify

• Subtract 7 from both sides

• Substitute 7 for M and simplify

What is the result of substituting M = -1 into the original equation?

• The equation does not hold

• The equation holds true

• The equation becomes undefined

• The equation results in a negative value