### Home > CCA2 > Chapter 3 > Lesson 3.2.4 > Problem3-104

3-104.

Solve the equations and inequalities below. Check your solutions, if possible. Homework Help ✎

1. $| 5 x + 8 | \geq - 4$

Note the absolute value. When is an absolute value greater than or equal to −4?

all real numbers

2. $x^2 + x − 20 < 0$

Factor, and solve for x. Since this is an inequality, these are the boundary points.

(x − 4)(x + 5) < 0
The boundary points are 4 and −5.

Plot your boundary points on a number line. Test a point in each region to see which region(s) make the inequality true.

−5 < x < 4

3. $2x^2 − 6x = −5$

This is a quadratic equation. Set it equal to 0. Then factor and use the Zero Product Property or use the Quadratic Formula to solve.

4. $\frac { 5 } { 9 } - \frac { x } { 3 } = \frac { 4 } { 9 }$

Fractions represent division. Multiply all terms by 9 to 'undo' the denominators.