Solving Equations by Graphing

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 equation involving absolute values?

Back

To solve an equation involving absolute values, you set up two separate equations: one for the positive case and one for the negative case.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values that can satisfy the equation, often due to contradictions.

Front

What is the solution to the equation |x - 6| + 4 = 10?

Back

x = 12 and x = 0.

Front

How do you determine the number of solutions for the equation 4|m| = -20?

Back

Since the absolute value cannot be negative, this equation has no solution.

Front

What is the process for solving linear equations?

Back

To solve linear equations, isolate the variable on one side of the equation using inverse operations.

Front

What is the solution to the equation -(1/4)x + 6 = (1/2)x + 3?

Back

x = 4.

Front

What does the equation |x + 8| = |x - 2| represent?

Back

This equation represents two cases: x + 8 = x - 2 and x + 8 = -(x - 2), leading to potential solutions.

Front

What is the solution to the equation |x + 8| = |x - 2|?

Back

x = -3.

Front

What is the solution to the equation |2x - 1| + 4 = 8?

Back

x = 2.5 and x = -1.5.