2.1 Solve Absolute Value eq

Front

What is the definition of 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 of the form |x| = a?

Back

To solve |x| = a, set up two equations: x = a and x = -a.

Front

What is the solution to the equation |x - 5| = 3?

Back

x = 8 or x = 2.

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 a negative number.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, move all other terms to the opposite side of the equation.

Front

Solve: |2x + 4| = 10

Back

x = 3 or x = -7.

Front

What is the first step in solving the equation 3|v + 8| − 15 = 6?

Back

Add 15 to both sides to isolate the absolute value: 3|v + 8| = 21.

Front

How do you check your solutions for absolute value equations?

Back

Substitute the solutions back into the original equation to verify if both sides are equal.

Front

Solve: |−2n| + 10 = −50

Back

No Solution.

Front

What is the solution to the equation 9|9 − 2p| = 81?

Back

p = 0 or p = 9.