Mastering Absolute Value Equations

What is the unique characteristic of absolute value equations?

• They only work with positive numbers.

• They cannot be solved algebraically.

• They involve the distance from zero.

• They always have one solution.

Under what condition can an absolute value equation be solved?

• When the variable term is zero.

• When the variable term is negative.

• When the constant term is zero or positive.

• When the constant term is negative.

What does the term 'opposite of c' refer to in absolute value equations?

• The reciprocal of c.

• The square of c.

• The negative value of c.

• The positive value of c.

Why do absolute value equations have two possible solutions?

• Because they are quadratic equations.

• Because they involve both positive and negative numbers.

• Because the absolute value represents distance from zero.

• Because they can be solved in two different ways.

What are the two possible solutions for the equation |x| = 8?

• x = -8 and x = 0

• x = 8 and x = -8

• x = 8 and x = 0

• x = 8 and x = 16

In the equation |x + 1| = 3, what are the two resulting equations?

• x + 1 = 3 and x + 1 = -3

• x + 1 = 3 and x - 1 = 3

• x - 1 = 3 and x - 1 = -3

• x + 1 = 3 and x + 1 = 0

What is the solution for the equation x + 1 = 3?

• x = -2

• x = 1

• x = 2

• x = 4

What is the solution for the equation x + 1 = -3?

• x = -4

• x = -1

• x = -2

• x = -3

In the equation |4x + 2| = 14, what is the first step to isolate the absolute value?

• Divide both sides by 2.

• Multiply both sides by 2.

• Add 2 to both sides.

• Subtract 2 from both sides.

What are the two possible solutions for the equation 4x = 12?

• x = -3 and x = -6

• x = 6 and x = -6

• x = 3 and x = 6

• x = 3 and x = -3