### Home > AC > Chapter 12 > Lesson 12.2.1 > Problem12-41

12-41.

Solve each equation or inequality below, if possible. Check your solution.

1. $−(x − 3)(x + 1) = 4$

2. $10 | x − 3 | > 40$

3. $(x − 5)^3 = 8$

Use a generic rectangle to multiply the factors together then distribute the negative and solve.

Set the equation equal to $0$. Then use a generic rectangle to factor and solve for $x$ using the Zero Product Property.

Solve for the absolute value then make two equations to remove the absolute value.

$x − 3 = 4$ or $x − 3 = −4$
$x = 7$ or $x = −1$

Test numbers to determine which region is the solution.

What number cubed equals $8$?