Solving Absolute Value and Literal Equations

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you solve an absolute value equation like |x| = a?

Back

You set up two equations: x = a and x = -a.

Front

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

Back

It means that the expression inside the absolute value cannot equal the given value, typically when the right side is negative.

Front

What is a literal equation?

Back

A literal equation is an equation that involves two or more variables and is solved for one variable in terms of the others.

Front

How do you isolate a variable in a literal equation?

Back

You perform inverse operations to both sides of the equation to get the variable by itself.

Front

What is the first step to solve the equation -2|x + 3| = -10?

Back

Divide by -2 on both sides.

Front

When do you set up two equations in an absolute value equation?

Back

You set up two equations after isolating the absolute value expression.

Front

What is the solution to the equation |2x - 1| = -5?

Back

No Solution, because absolute values cannot be negative.

Front

How do you solve the equation am = n + p for a?

Back

a = \frac{n + p}{m}.

Front

What is the first step to solve the equation |x + 2| + 3 = 4?

Back

Subtract 3 from both sides.