Solving Linear and Absolute Value Equations

The video tutorial explains how to solve absolute value equations by first isolating the absolute value expression. The instructor demonstrates dividing by a coefficient to simplify the equation, then solving for x by considering both positive and negative cases. The process involves adding and dividing terms to find the solution, concluding with the final values of x.

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

• Subtract a constant from both sides

• Multiply both sides by a constant

• Isolate the absolute value

• Add a constant to both sides

What are the two cases to consider when solving absolute value equations?

• Absolute value equals zero and positive

• Absolute value equals positive and negative

• Absolute value equals zero and negative

• Absolute value equals positive and zero

Why is it important to isolate the absolute value in an equation?

• To set up two separate equations

• To determine the sign of the solution

• To apply the quadratic formula

• To simplify the equation

What operation is performed to isolate the absolute value in the equation 2|3x - 2| = 14?

• Subtract 2 from both sides

• Multiply both sides by 2

• Divide both sides by 2

• Add 2 to both sides

After isolating the absolute value, what are the two equations formed from |3x - 2| = 7?

• 3x - 2 = 7 and 3x - 2 = -7

• 3x - 2 = 0 and 3x - 2 = 7

• 3x - 2 = 7 and 3x + 2 = 7

• 3x + 2 = 7 and 3x - 2 = 0

What is the next step after setting up the equations 3x - 2 = 7 and 3x - 2 = -7?

• Subtract 2 from both sides

• Divide both sides by 3

• Add 2 to both sides

• Multiply both sides by 3

What is the solution for x in the equation 3x - 2 = 7?

• x = 7

• x = 9

• x = 5

• x = 3

What is the solution for x in the equation 3x - 2 = -7?

• x = -3

• x = -5/3

• x = -9

• x = -7/3

What is the final step in solving the equation 3x = 9?

• Divide both sides by 3

• Subtract 3 from both sides

• Add 3 to both sides

• Multiply both sides by 3

What is the final step in solving the equation 3x = -5?

• Divide both sides by 3

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 3