Question

date: _____ per: _____
this is a 2-page document!
directions: graph each inequality on the number line.

1. $x < -2$
2. $u \geq 9$
3. $v \leq -13$
4. $c > 4$
5. $7 \leq k$
6. $-20 > r$

directions: translate each inequality, then graph.

1. \a number is greater than -7.\
2. \a number is less than or equal to 1.\
3. \a number is at most 12.\
4. \a number is 3 at minimum.\
5. \a number is no more than 0.\
6. \a number is at least -18.\

directions: state whether the number is a solution to the given inequality.

1. $x \geq -17; -14$
2. $m < 5; 5$
3. $n > \frac{9}{16}; \frac{7}{12}$

directions: solve each inequality and graph the solution on the number line.

1. $a - 5 < -1$

Explanation:

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Section 1: Graph the Inequality

Step1: Graph $x < -2$

• Locate $-2$ on the number line. Use an open circle (since $x$ cannot equal $-2$), then shade all values to the left of $-2$.

Step2: Graph $u \geq 9$

• Locate $9$ on the number line. Use a closed circle (since $u$ can equal $9$), then shade all values to the right of $9$.

Step3: Graph $v \leq -13$

• Locate $-13$ on the number line. Use a closed circle (since $v$ can equal $-13$), then shade all values to the left of $-13$.

Step4: Graph $c > 4$

• Locate $4$ on the number line. Use an open circle (since $c$ cannot equal $4$), then shade all values to the right of $4$.

Step5: Graph $7 \leq k$

• Locate $7$ on the number line. Use a closed circle (since $k$ can equal $7$), then shade all values to the right of $7$.

Step6: Graph $-20 > r$ (rewrite as $r < -20$)

• Locate $-20$ on the number line. Use an open circle (since $r$ cannot equal $-20$), then shade all values to the left of $-20$.

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Section 2: Translate & Graph

Step7: Translate "A number is greater than -7"

Let $n$ = the number. Inequality: $n > -7$

• Graph: Open circle at $-7$, shade right.

Step8: Translate "A number is less than or equal to 1"

Let $n$ = the number. Inequality: $n \leq 1$

• Graph: Closed circle at $1$, shade left.

Step9: Translate "A number is at most 12"

"At most" means $\leq$. Inequality: $n \leq 12$

• Graph: Closed circle at $12$, shade left.

Step10: Translate "A number is 3 at minimum"

"At minimum" means $\geq$. Inequality: $n \geq 3$

• Graph: Closed circle at $3$, shade right.

Step11: Translate "A number is no more than 0"

"No more than" means $\leq$. Inequality: $n \leq 0$

• Graph: Closed circle at $0$, shade left.

Step12: Translate "A number is at least -18"

"At least" means $\geq$. Inequality: $n \geq -18$

• Graph: Closed circle at $-18$, shade right.

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Section 3: Check Solution Validity

Step13: Check $x \geq -17; -14$

$-14$ is greater than $-17$, so it satisfies $x \geq -17$.

Step14: Check $m < 5; 5$

$5$ is not less than $5$, so it does not satisfy $m < 5$.

Step15: Check $n > \frac{9}{16}; \frac{7}{12}$

Convert to common denominators: $\frac{9}{16} = \frac{27}{48}$, $\frac{7}{12} = \frac{28}{48}$. $\frac{28}{48} > \frac{27}{48}$, so $\frac{7}{12}$ satisfies $n > \frac{9}{16}$.

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Section 4: Solve & Graph

Step16: Solve $a - 5 < -1$

Add 5 to both sides: $a < -1 + 5$ → $a < 4$

• Graph: Open circle at $4$, shade left.

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Answer:

Section 1 (Graphs):

1. Open circle at $-2$, shade left.
2. Closed circle at $9$, shade right.
3. Closed circle at $-13$, shade left.
4. Open circle at $4$, shade right.
5. Closed circle at $7$, shade right.
6. Open circle at $-20$, shade left.

Section 2 (Translate & Graph):

1. Inequality: $n > -7$; Open circle at $-7$, shade right.
2. Inequality: $n \leq 1$; Closed circle at $1$, shade left.
3. Inequality: $n \leq 12$; Closed circle at $12$, shade left.
4. Inequality: $n \geq 3$; Closed circle at $3$, shade right.
5. Inequality: $n \leq 0$; Closed circle at $0$, shade left.
6. Inequality: $n \geq -18$; Closed circle at $-18$, shade right.

Section 3 (Solution Check):

1. Yes
2. No
3. Yes

Section 4 (Solve & Graph):

1. Solution: $a < 4$; Open circle at $4$, shade left.