How do you solve the equation $$|x| = a$$ where $$a >= 0$$ ?

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

Solve the equation $$|4 + 2x| - 1 = 19$$ .

The solution is $$x = 8, -12$$ .

What does the equation $$|x + 10| = 11$$ represent?

It represents two possible equations: $$x + 10 = 11$$ and $$x + 10 = -11$$ .

Solve the equation $$|10x + 1| = 41$$ .

The solution is $$x = 4, -\frac{21}{10}$$ .

Solve the equation $$|-3x - 6| = 15$$ .

The solution is $$x = -7, 3$$ .

How do you interpret the solutions of an absolute value equation?

The solutions represent the values of the variable that make the original equation true, considering both positive and negative scenarios.

Solve the equation $$9 + |8x + 8| = 33$$ .

The solution is $$x = 2, -4$$ .

What is the general form of an absolute value equation?

The general form is $$|expression| = constant$$ .

What happens if the absolute value equation equals a negative number?

If $$|expression| = negative number$$ , there are no solutions because absolute values cannot be negative.

How can you check your solutions for an absolute value equation?

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

What is the relationship between absolute value and distance?

Absolute value measures the distance of a number from zero, regardless of direction.

What is the solution set for the equation $$|x| = 0$$ ?

The solution set is $$x = 0$$ .

Solving Absolute Value Equations Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the first step in solving an absolute value equation?

Back

The first step is to isolate the absolute value expression on one side of the equation.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the significance of the absolute value in an equation?

Back

The absolute value indicates that the solution can be either positive or negative, reflecting the distance from zero.

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