Multi-Step Inequalities 2

Question 1 of 4

Find the inequality that represents all possible

a

$a$ values

a + 7 \geq 3 a - 4

$a+7≥3a-4$

1. $a \geq - 5 \frac{1}{2}$ $a≥-5 1/2$
2. $a \leq - 5 \frac{1}{2}$ $a≤-5 1/2$
3. $a \geq 5 \frac{1}{2}$ $a≥5 1/2$
4. $a \leq 5 \frac{1}{2}$ $a≤5 1/2$

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If a negative value is multiplied to both sides of an inequality, the inequality flips.

- x

$-x$

<

$<$

a

$a$ becomes

x

$x$

>

$>$

- a

$-a$

First, make sure that only

a

$a$ is on the left side

$a + 7$ $a+7$	$\geq$ $≥$	$3 a - 4$ $3a-4$
$a + 7$ $a+7$ $- 7$ $-7$	$\geq$ $≥$	$3 a - 4$ $3a-4$ $- 7$ $-7$	Subtract $7$ $7$ from both sides
$a$ $a$ $- 3 a$ $-3a$	$\geq$ $≥$	$3 a - 11$ $3a-11$ $- 3 a$ $-3a$	Subtract $3 a$ $3a$ from both sides
$- 2 a$ $-2a$ $\div (- 2)$ $divide(-2)$	$\geq$ $≥$	$- 11$ $-11$ $\div (- 2)$ $divide(-2)$	Divide both sides by $- 2$ $-2$

$a$ $a$	$\leq$ $≤$	$5 \frac{1}{2}$ $5 1/2$	Flip the inequality

a \leq 5 \frac{1}{2}

$a≤5 1/2$

Question 2 of 4

Choose the number line that represents the inequality

- 7 (y + 2) + 8 y

$-7(y+2)+8y$

<

$<$

- 14

$-14$

1.
2.
3.
4.

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Representing Inequalities in the Number Line

Greater than (

>

$>$ )

Greater than or equal (

\geq

$≥$ )

Less than (

<

$<$ )

Less than or equal (

\leq

$≤$ )

First, make sure that only

y

$y$ is on the left side

$- 7 (y + 2) + 8 y$ $-7(y+2)+8y$	$<$ $<$	$- 14$ $-14$
$- 7 y - 14 + 8 y$ $-7y-14+8y$	$<$ $<$	$- 14$ $-14$	Expand
$y - 14$ $y-14$	$<$ $<$	$- 14$ $-14$	Combine like terms
$y - 14$ $y-14$ $+ 14$ $+14$	$<$ $<$	$- 14$ $-14$ $+ 14$ $+14$	Add $14$ $14$ to both sides
$y$ $y$	$<$ $<$	$0$ $0$

The given inequality has a less than (

<

$<$ ) sign.

Hence, place an empty circle above $0$ $0$ and attach an arrow pointing to the left to represent all values less than

0

$0$ .

Question 3 of 4

Choose the number line that represents the inequality

\frac{x - 2}{2}

$(x-2)/2$

>

$>$

\frac{x + 1}{4}

$(x+1)/4$

1.
2.
3.
4.

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Representing Inequalities in the Number Line

Greater than (

>

$>$ )

Greater than or equal (

\geq

$≥$ )

Less than (

<

$<$ )

Less than or equal (

\leq

$≤$ )

First, make sure that only

x

$x$ is on the left side

$\frac{x - 2}{2}$ $(x-2)/2$	$>$ $>$	$\frac{x + 1}{4}$ $(x+1)/4$

$4 (x - 2)$ $4(x-2)$	$>$ $>$	$2 (x + 1)$ $2(x+1)$	Cross multiply
$4 x - 8$ $4x-8$	$>$ $>$	$2 x + 2$ $2x+2$	Expand
$4 x - 8$ $4x-8$ $- 2 x$ $-2x$	$>$ $>$	$2 x + 2$ $2x+2$ $- 2 x$ $-2x$	Subtract $2 x$ $2x$ from both sides
$2 x - 8$ $2x-8$ $+ 8$ $+8$	$>$ $>$	$2$ $2$ $+ 8$ $+8$	Add $8$ $8$ to both sides
$2 x$ $2x$ $\div 2$ $divide2$	$>$ $>$	$10$ $10$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$x$ $x$	$>$ $>$	$5$ $5$

The given inequality has a greater than (

>

$>$ ) sign.

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

5

$5$ .

Question 4 of 4

Simplify

\frac{3 x}{5} + 2 \leq \frac{2 x}{5}

$(3x)/5+2≤(2x)/5$

1. $x \leq - 10$ $x≤-10$
2. $x \leq 10$ $x≤10$
3. $x \geq 10$ $x≥10$
4. $x \geq - 10$ $x≥-10$

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Representing Inequalities in the Number Line

Greater than (

>

$>$ )

Greater than or equal (

\geq

$≥$ )

Less than (

<

$<$ )

Less than or equal (

\leq

$≤$ )

First, make sure that only

x

$x$ is on the left side

$\frac{3 x}{5} + 2$ $(3x)/5+2$	$\leq$ $≤$	$\frac{2 x}{5}$ $(2x)/5$

$(\frac{3 x}{5} + 2)$ $((3x)/5+2)$ $\times 5$ $times5$	$\leq$ $≤$	$(\frac{2 x}{5})$ $((2x)/5)$ $\times 5$ $times5$	Multiply both sides by $5$ $5$

$3 x + 10$ $3x+10$ $- 2 x$ $-2x$	$\leq$ $≤$	$2 x$ $2x$ $- 2 x$ $-2x$	Subtract $2 x$ $2x$ from both sides
$x + 10$ $x+10$ $- 10$ $-10$	$\leq$ $≤$	$0$ $0$ $- 10$ $-10$	Subtract $10$ $10$ from both sides
$x$ $x$	$\leq$ $≤$	$- 10$ $-10$

x \leq - 10

$x≤-10$

Multi-Step Inequalities 2

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Quiz summary

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1. Question

Hint

Great Work!

2. Question

Hint

Fantastic!

Representing Inequalities in the Number Line

3. Question

Hint

Well Done!

Representing Inequalities in the Number Line

4. Question

Hint

Fantastic!

Representing Inequalities in the Number Line

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