Multi-Step Inequalities 1

Question 1 of 4

Choose the number line that represents the inequality

2 (x - 1) \leq 6

$2(x-1)≤6$

1.
2.
3.
4.

Incorrect

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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

$2 (x - 1)$ $2(x-1)$	$\leq$ $≤$	$6$ $6$
$2 x - 2$ $2x-2$	$\leq$ $≤$	$6$ $6$	Expand
$2 x - 2$ $2x-2$ $+ 2$ $+2$	$\leq$ $≤$	$6$ $6$ $+ 2$ $+2$	Add $2$ $2$ to both sides
$2 x$ $2x$	$\leq$ $≤$	$8$ $8$
$2 x$ $2x$ $\div 2$ $divide2$	$\leq$ $≤$	$8$ $8$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$x$ $x$	$\leq$ $≤$	$4$ $4$

The given inequality has a less than or equal to (

\leq

$≤$ ) sign.

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

4

$4$ .

Question 2 of 4

Choose the number line that represents the inequality

4 (x + 2) \geq 12

$4(x+2)≥12$

1.
2.
3.
4.

Incorrect

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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

$4 (x + 2)$ $4(x+2)$	$\geq$ $≥$	$12$ $12$
$4 x + 8$ $4x+8$	$\geq$ $≥$	$12$ $12$	Expand
$4 x + 8$ $4x+8$ $- 8$ $-8$	$\geq$ $≥$	$12$ $12$ $- 8$ $-8$	Subtract $8$ $8$ from both sides
$4 x$ $4x$	$\geq$ $≥$	$4$ $4$
$4 x$ $4x$ $\div 4$ $divide4$	$\geq$ $≥$	$4$ $4$ $\div 4$ $divide4$	Divide both sides by $4$ $4$
$x$ $x$	$\geq$ $≥$	$1$ $1$

The given inequality has a greater than or equal to (

\geq

$≥$ ) sign.

Hence, place a solid circle above $1$ $1$ and attach an arrow pointing to the right to represent all values greater than

1

$1$ .

Question 3 of 4

Choose the number line that represents the inequality

\frac{x - 8}{5} \geq - 2

$(x-8)/5≥-2$

1.
2.
3.
4.

Incorrect

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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

$\frac{x - 8}{5}$ $(x-8)/5$	$\geq$ $≥$	$- 2$ $-2$

$\frac{x - 8}{5}$ $(x-8)/5$ $\times 5$ $times5$	$\geq$ $≥$	$- 2$ $-2$ $\times 5$ $times5$	Multiply both sides by $5$ $5$

$x - 8$ $x-8$	$\geq$ $≥$	$- 10$ $-10$	$\frac{5}{5} = 1$ $5/5=1$

$x - 8$ $x-8$ $+ 8$ $+8$	$\geq$ $≥$	$- 10$ $-10$ $+ 8$ $+8$	Add $8$ $8$ to both sides
$x$ $x$	$\geq$ $≥$	$- 2$ $-2$

The given inequality has a greater than or equal to (

\geq

$≥$ ) sign.

Hence, place a solid circle above $- 2$ $-2$ and attach an arrow pointing to the right to represent all values greater than

- 2

$-2$ .

Question 4 of 4

Choose the number line that represents the inequality

\frac{1 - 2 x}{3}

$(1-2x)/3$

<

$<$

1

$1$

1.
2.
3.
4.

Incorrect

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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

$\frac{1 - 2 x}{3}$ $(1-2x)/3$	$<$ $<$	$1$ $1$

$\frac{1 - 2 x}{3}$ $(1-2x)/3$ $\times 3$ $times3$	$<$ $<$	$1$ $1$ $\times 3$ $times3$	Multiply both sides by $5$ $5$

$1 - 2 x$ $1-2x$ $- 1$ $-1$	$<$ $<$	$3$ $3$ $- 1$ $-1$	Subtract $1$ $1$ from both sides
$- 2 x$ $-2x$ $\div (- 2)$ $divide(-2)$	$<$ $<$	$2$ $2$ $\div (- 2)$ $divide(-2)$	Divide both sides by $- 2$ $-2$
$x$ $x$	$>$ $>$	$- 1$ $-1$	Flip the inequality

The given inequality has a greater than (

>

$>$ ) sign.

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

- 1

$-1$ .

Multi-Step Inequalities 1

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Quiz summary

Information

1. Question

Hint

Correct!

Representing Inequalities in the Number Line

2. Question

Hint

Keep Going!

Representing Inequalities in the Number Line

3. Question

Hint

Excellent!

Representing Inequalities in the Number Line

4. Question

Hint

Nice Job!

Representing Inequalities in the Number Line

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