How to solve absolute value equations - Algebra

Card 0 of 738

Question

Solve the absolute value equation:

$\left | \frac{x-4}{3} \right| = \left | x +2 \right|$

Answer

An equation that equates two absolute value functions allows us to choose one of the absolute value functions and treat it as the constant. We then separate the equation into the "positive" version, $\tiny \small \frac{x-4}{3}=x+2$ , and the "negative" version, $\tiny \small \frac{x-4}{3} = -(x+2)$ . Solving each equation, we obtain the solutions, and $\tiny \tiny -\frac{1}{2}$ , respectively.

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Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

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Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

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Question

What is the solution set of this equation?

$\left | 3x-7\right |+7 = -6$

Answer

$\left | 3x-7\right |+7 = -6$

To find a solution, subtract first to isolate the absolute value expression.

$\left | 3x-7\right | = -13$

There is no value of that makes this true, as no number has a negative absolute value. The equation has no solution.

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Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

Question

What is the solution set of this equation?

$\left | 3x-7\right |+7 = -6$

Answer

$\left | 3x-7\right |+7 = -6$

To find a solution, subtract first to isolate the absolute value expression.

$\left | 3x-7\right | = -13$

There is no value of that makes this true, as no number has a negative absolute value. The equation has no solution.

Compare your answer with the correct one above

Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

Question

What is the solution set of this equation?

$\left | 3x-7\right |+7 = -6$

Answer

$\left | 3x-7\right |+7 = -6$

To find a solution, subtract first to isolate the absolute value expression.

$\left | 3x-7\right | = -13$

There is no value of that makes this true, as no number has a negative absolute value. The equation has no solution.

Compare your answer with the correct one above

Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$-3x \div (-3) = -57 \div (-3)$

$-3x \div (-3) = 27 \div (-3)$

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Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$5x \div 5 = -50 \div 5$

$5x \div 5 = 80 \div 5$

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Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$5x \div 5 = -50 \div 5$

$5x \div 5 = 80 \div 5$

Compare your answer with the correct one above

Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$-3x \div (-3) = -57 \div (-3)$

$-3x \div (-3) = 27 \div (-3)$

Compare your answer with the correct one above

Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$-3x \div (-3) = -57 \div (-3)$

$-3x \div (-3) = 27 \div (-3)$

Compare your answer with the correct one above

Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$-3x \div (-3) = -57 \div (-3)$

$-3x \div (-3) = 27 \div (-3)$

Compare your answer with the correct one above

Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

Question

Solve for :

Answer

Rewrite as a compound statement:

or

Solve each separately:

$5x \div 5 = -50 \div 5$

$5x \div 5 = 80 \div 5$

Compare your answer with the correct one above

Question

Solve the absolute value equation:

$\left | \frac{x-4}{3} \right| = \left | x +2 \right|$

Answer

An equation that equates two absolute value functions allows us to choose one of the absolute value functions and treat it as the constant. We then separate the equation into the "positive" version, $\tiny \small \frac{x-4}{3}=x+2$ , and the "negative" version, $\tiny \small \frac{x-4}{3} = -(x+2)$ . Solving each equation, we obtain the solutions, and $\tiny \tiny -\frac{1}{2}$ , respectively.

Compare your answer with the correct one above

Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

Question

Solve for :

Answer

The absolute value of a number can never be a negative number. Therefore, no value of can make a true statement.

Compare your answer with the correct one above

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