Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve an absolute value equation of the form |x| = a?

Back

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

Front

What is the first step in solving an absolute value equation like |4x - 1| = 5?

Back

The first step is to isolate the absolute value expression, if necessary, and then set up two equations based on the definition of absolute value.

Front

What are the solutions to the equation |3x + 2| = 5?

Back

The solutions are x = 1 and x = -2.333... (or -7/3).

Front

How do you handle absolute value equations that include additional constants, such as |2x - 1| + 4 = 8?

Back

First, isolate the absolute value expression by subtracting the constant from both sides, then solve the resulting absolute value equation.

Front

What is the solution to the equation |5x| = 40?

Back

The solutions are x = 8 and x = -8.

Front

What does the equation |2x - 1| = 9 represent in terms of distance?

Back

It represents that the distance between 2x - 1 and 0 is equal to 9.

Front

What is the significance of the two solutions in absolute value equations?

Back

The two solutions represent the two possible values that satisfy the equation, reflecting the property that absolute value can yield both positive and negative results.

Front

How can you check if your solutions to an absolute value equation are correct?

Back

You can check by substituting the solutions back into the original equation to see if both sides are equal.

Front

What is the general form of an absolute value equation?

Back

The general form is |expression| = constant, where 'expression' can be any algebraic expression.

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