Solving Absolute Value Equations

Front

What is an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation |A| = B, you set up two equations: A = B and A = -B, then solve for the variable.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value (e.g., |x| = -5 has no solution).

Front

Solve |x + 3| = 7.

Back

x + 3 = 7 or x + 3 = -7; solutions are x = 4 and x = -10.

Front

What is the first step in solving |2x - 5| = 3?

Back

Set up two equations: 2x - 5 = 3 and 2x - 5 = -3.

Front

Solve |x - 1| + 4 = 10.

Back

|x - 1| = 6; solutions are x = 7 and x = -5.

Front

What is the solution to |3x + 2| = 0?

Back

The solution is x = -2/3, since the absolute value equals zero only when the expression inside is zero.

Front

Solve |x| = 5.

Back

x = 5 or x = -5.

Front

What does |x - 4| < 2 represent?

Back

It represents the values of x that are within 2 units of 4, leading to the inequalities 2 < x < 6.

Front

How do you graph an absolute value function?

Back

An absolute value function, like y = |x|, forms a V shape on the graph, opening upwards.