Absolute Value Equations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the general form of an absolute value equation?

Back

An absolute value equation is typically expressed as |A| = B, where A is an expression involving a variable and B is a non-negative number.

Front

How do you solve the equation |x| = a?

Back

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

Front

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

Back

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

Front

What is the graphical representation of an absolute value function?

Back

The graph of an absolute value function is a V-shaped graph that opens upwards.

Front

How do you solve the equation |2x + 1| = 7?

Back

Set up two equations: 2x + 1 = 7 and 2x + 1 = -7. Solve for x to get x = 3 and x = -4.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, you need to move all other terms to the opposite side of the equation.

Front

What is the solution to the equation |x + 4| = 0?

Back

The solution is x = -4, since the absolute value is zero only when the expression inside is zero.

Front

What is the relationship between absolute value and distance?

Back

The absolute value represents the distance of a number from zero, which is always a non-negative value.