Question

date
practice 19

1. for parts (a)-(d), consider the inequality $x + 6 < -19$.

a. solve the related equation to find the boundary number.
b. test a number for $x$ to determine which region to shade.
c. graph the solution set on the number line.
d. what is the solution set of the inequality?

1. for parts (a)-(d), consider the inequality $-13 \leq x - 5$.

a. solve the related equation to find the boundary number.

Explanation:

Step1: Solve related equation for 1(a)

Set $x + 6 = -19$. Subtract 6 from both sides:
$x = -19 - 6$
$x = -25$

Step2: Test value for 1(b)

Pick $x = 0$ (greater than -25):
$0 + 6 = 6$, $6 < -19$ is false. Pick $x = -30$ (less than -25):
$-30 + 6 = -24$, $-24 < -19$ is true. Shade left of -25.

Step3: Graph for 1(c)

Draw an open circle at $x=-25$ on the number line, then shade all values to the left of this point.

Step4: Solution set for 1(d)

All real numbers less than -25:
$x < -25$

Step5: Solve related equation for 2(a)

Set $-13 = x - 5$. Add 5 to both sides:
$x = -13 + 5$
$x = -8$

Answer:

1. a. $x=-25$
2. b. Shade the region left of $-25$ (tested $x=-30$ works)
3. c. Open circle at $-25$, shade all values to the left on the given number line
4. d. All real numbers $x$ where $x < -25$
5. a. $x=-8$