Compound Inequalities 3

Question 1 of 3

Find the inequality that represents all possible

n

$n$ values

- 6

$-6$

<

$<$

4 n + 10

$4n+10$

<

$<$

2

$2$

1. $4$ $4$ $>$ $>$ $n$ $n$ $>$ $>$ $2$ $2$
2. $- 4$ $-4$ $<$ $<$ $n$ $n$ $<$ $<$ $- 2$ $-2$
3. $4$ $4$ $>$ $>$ $n$ $n$ $>$ $>$ $2$ $2$
4. $- 4$ $-4$ $<$ $<$ $n$ $n$ $<$ $<$ $- 2$ $-2$

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A compound inequality consists of two inequalities joined together by AND or OR.

First, make sure that

x

$x$ is left alone in the middle

$- 6$ $-6$ $<$ $<$ $4 n + 10$ $4n+10$	$<$ $<$	$2$ $2$
$- 6$ $-6$ $- 10$ $-10$ $<$ $<$ $4 n + 10$ $4n+10$ $- 10$ $-10$	$<$ $<$	$2$ $2$ $- 10$ $-10$	Subtract $10$ $10$ from all sections
$- 16$ $-16$ $\div 4$ $divide4$ $<$ $<$ $4 n$ $4n$ $\div 4$ $divide4$	$<$ $<$	$- 8$ $-8$ $\div 4$ $divide4$	Divide all sections by $4$ $4$
$- 4$ $-4$ $<$ $<$ $n$ $n$	$<$ $<$	$- 2$ $-2$

- 4

$-4$

<

$<$

n

$n$

<

$<$

- 2

$-2$

Question 2 of 3

Choose the number line that represents the inequality

3 x + 5

$3x+5$

<

$<$

2

$2$ OR

2 x - 7 \geq 1

$2x-7≥1$

1.
2.
3.
4.

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A compound inequality consists of two inequalities joined together by AND or OR.

Solve the two inequalities seperately.

Solve for

3 x + 5

$3x+5$

<

$<$

2

$2$ first.

$3 x + 5$ $3x+5$	$<$ $<$	$2$ $2$
$3 x + 5$ $3x+5$ $- 5$ $-5$	$<$ $<$	$2$ $2$ $- 5$ $-5$	Subtract $5$ $5$ from both sides
$3 x$ $3x$ $\div 3$ $divide3$	$<$ $<$	$- 3$ $-3$ $\div 3$ $divide3$	Divide both sides by $3$ $3$
$x$ $x$	$<$ $<$	$- 1$ $-1$

The given inequality has a less than (

<

$<$ ) sign.

Hence, place a empty circle above $- 1$ $-1$ and attach an arrow pointing to the left to represent all values less than

- 1

$-1$ .

Next, solve for

2 x - 7 \geq 1

$2x-7≥1$ .

$2 x - 7$ $2x-7$	$\geq$ $≥$	$1$ $1$
$2 x - 7$ $2x-7$ $+ 7$ $+7$	$\geq$ $≥$	$1$ $1$ $+ 7$ $+7$	Add $7$ $7$ to both sides
$2 x$ $2x$ $\div 2$ $divide2$	$\geq$ $≥$	$8$ $8$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$x$ $x$	$\geq$ $≥$	$4$ $4$

The given inequality has a greater than or equal to (

\geq

$≥$ ) sign.

Hence, place a solid circle above $4$ $4$ and attach an arrow pointing to the right to represent all values greater than

95

$95$ .

Finally, combine the two number lines.

Question 3 of 3

Choose the number line that represents the inequality

y + 11

$y+11$

<

$<$

8

$8$ OR

- 9 y

$-9y$

<

$<$

- 45

$-45$

1.
2.
3.
4.

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A compound inequality consists of two inequalities joined together by AND or OR.

Solve the two inequalities seperately.

Solve for

y + 11

$y+11$

<

$<$

8

$8$ first.

$y + 11$ $y+11$	$<$ $<$	$8$ $8$
$y + 11$ $y+11$ $- 11$ $-11$	$<$ $<$	$8$ $8$ $- 11$ $-11$	Subtract $11$ $11$ from both sides
$y$ $y$	$<$ $<$	$- 3$ $-3$

The given inequality has a less than (

<

$<$ ) sign.

Hence, place a empty circle above $- 3$ $-3$ and attach an arrow pointing to the left to represent all values less than

- 3

$-3$ .

Next, solve for

- 9 y

$-9y$

<

$<$

- 45

$-45$ .

$- 9 y$ $-9y$	$<$ $<$	$- 45$ $-45$
$- 9 y$ $-9y$ $\div (- 9)$ $divide(-9)$	$<$ $<$	$- 45$ $-45$ $\div (- 9)$ $divide(-9)$	Divide both sides by $- 9$ $-9$
$y$ $y$	$>$ $>$	$5$ $5$	Flip the inequality

The given inequality has a greater than (

>

$>$ ) sign.

Hence, place a solid circle above $5$ $5$ and attach an arrow pointing to the right to represent all values greater than

5

$5$ .

Finally, combine the two number lines.

Compound Inequalities 3

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3. Question

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