Question

i can write and interpret inequalities.

1. write two statements of inequality.

a
b

1. write two statements of inequality

a
b

1. translate the inequality to a written statement.

-19 < -14

1. translate the inequality to a written statement.

-1 < 4

1. determine the inequality sign, graph both points, and then describe the relationship to one another.

-7

1. determine the inequality sign, graph both points, and then describe the relationship to one another.

-1\frac{1}{2} \frac{5}{3}

Explanation:

Step1: Analyze Q34 number line

The closed dots are at $x=-3$ and $x=3$.

a. Left dot inequality

$x \leq -3$

b. Right dot inequality

$x \geq 3$

Step2: Analyze Q35 number line

Closed dots are at $x=-4$ and $x=0$.

a. Left dot inequality

$x \leq -4$

b. Right dot inequality

$x \geq 0$

Step3: Translate Q36 inequality

Interpret $-19 < -14$:
"Negative nineteen is less than negative fourteen."

Step4: Translate Q37 inequality

Interpret $-1 < 4$:
"Negative one is less than four."

Step5: Solve Q38 inequality

Compare $-7$ and $-6.9$:
On a number line, $-7$ is left of $-6.9$, so $-7 < -6.9$.
Graph: Plot closed dots at $-7$ and $-6.9$; $-7$ is to the left of $-6.9$, meaning $-7$ is smaller than $-6.9$.

Step6: Solve Q39 inequality

Convert to decimals: $-1\frac{1}{2}=-1.5$, $\frac{5}{3}\approx1.67$.
$-1.5$ is left of $1.67$ on the number line, so $-1\frac{1}{2} < \frac{5}{3}$.
Graph: Plot closed dots at $-1.5$ and $\frac{5}{3}$; $-1\frac{1}{2}$ is to the left of $\frac{5}{3}$, meaning $-1\frac{1}{2}$ is smaller than $\frac{5}{3}$.

Answer:

34.
a. $x \leq -3$
b. $x \geq 3$

35.
a. $x \leq -4$
b. $x \geq 0$

1. Negative nineteen is less than negative fourteen.

1. Negative one is less than four.

1. Inequality: $-7 < -6.9$; Graph: Closed dot at $-7$ (left) and $-6.9$ (right); Relationship: $-7$ is less than $-6.9$.

1. Inequality: $-1\frac{1}{2} < \frac{5}{3}$; Graph: Closed dot at $-1\frac{1}{2}$ (left) and $\frac{5}{3}$ (right); Relationship: $-1\frac{1}{2}$ is less than $\frac{5}{3}$.