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

3-104.

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

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

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

all real numbers

1. $x^2 + x − 20 < 0$

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

1. $2x^2 − 6x = −5$

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.

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

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