Solving Absolute Value Equations

The video tutorial explains how to solve absolute value equations. It begins by introducing the problem and then outlines a step-by-step process. First, isolate the absolute value expression. Next, check if the equation equals a negative number, which would mean no solution. Then, rewrite the equation as two separate equations, one for the positive and one for the negative solution. Solve both equations using inverse operations. Finally, verify the solutions by substituting them back into the original equation to ensure they satisfy it.

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

• Check if the equation equals zero

• Isolate the absolute value expression

• Rewrite the equation as two separate equations

• Verify the solutions

Why can't an absolute value equation equal a negative number?

• Because it would have infinite solutions

• Because it would have no solutions

• Because it would result in a complex number

• Because absolute values are always positive

What do you do after isolating the absolute value expression?

• Check if the equation equals a negative number

• Verify the solutions

• Solve the equation directly

• Rewrite the equation as a single equation

How do you rewrite an absolute value equation?

• As a single equation

• As two separate equations

• As a quadratic equation

• As a linear equation

What are the two equations derived from |X - 2| = 7?

• X - 2 = 7 and X - 2 = -7

• X + 2 = 7 and X + 2 = -7

• X - 2 = 0 and X - 2 = 14

• X + 2 = 0 and X + 2 = 14

What operation is used to solve the equation X - 2 = 7?

• Multiply both sides by 2

• Add 2 to both sides

• Divide both sides by 2

• Subtract 2 from both sides

What is the solution to the equation X - 2 = 7?

• X = -9

• X = -5

• X = 9

• X = 5

What is the solution to the equation X - 2 = -7?

• X = 5

• X = 9

• X = -5

• X = -9

What should you do after solving both equations?

• Check if the solutions are correct

• Rewrite the equations

• Check if the equation equals a negative number

• Isolate the absolute value expression

How do you verify the solution X = 9?

• Plug X = 9 into the original equation

• Plug X = 9 into a different equation

• Check if X = 9 is a positive number

• Check if X = 9 is a negative number