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

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

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

The solution set is $${0}$$ , as the only number whose absolute value is zero is zero itself.

What is the solution to the equation $$|x + 3| = 5$$ ?

The solutions are $$x = 2$$ and $$x = -8$$ .

What is the solution to the equation $$|2x + 5| = 9$$ ?

The solutions are $$x = 2$$ and $$x = -7$$ .

What is the graphical representation of an absolute value function?

The graph of an absolute value function is a V-shape, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

What is the significance of the constant on the right side of an absolute value equation?

The constant on the right side of an absolute value equation indicates the distance from the value inside the absolute value to zero.

How do you solve $$|3x - 4| = 8$$ ?

Set up two equations: $$3x - 4 = 8$$ and $$3x - 4 = -8$$ , then solve for $$x$$ to get $$x = 4$$ and $$x = -\frac{4}{3}$$ .

What is the solution to the equation $$|x - 4| = -5$$ ?

There is no solution, as absolute values cannot be negative.

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

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

What does the term 'extraneous solution' mean?

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

What is the solution to the equation $$|2x + 5| = 11$$ ?

The solutions are $$x = 3$$ and $$x = -8$$ .

Linear equations (one variable) Flashcards

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