Two Step Inequalities

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Question 1 of 3

Choose the number line that represents the inequality

4 m + 5 - 3 m \geq - 9

$4m+5-3m≥-9$

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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

m

$m$ is on the left side

$4 m + 5 - 3 m$ $4m+5-3m$	$\geq$ $≥$	$- 9$ $-9$
$m + 5$ $m+5$	$\geq$ $≥$	$- 9$ $-9$	Combine like terms
$m + 5$ $m+5$ $- 5$ $-5$	$\geq$ $≥$	$- 9$ $-9$ $- 5$ $-5$	Subtract $5$ $5$ from both sides
$m$ $m$	$\geq$ $≥$	$- 14$ $-14$

The given inequality has a greater than or equal to (

\geq

$≥$ ) sign.

Hence, place a solid circle above $- 14$ $-14$ and attach an arrow pointing to the right to represent all values greater than

- 14

$-14$ .

Question 2 of 3

Find the inequality that represents all possible

m

$m$ values

- \frac{m}{10}

$-m/10$

>

$>$

\frac{1}{2}

$1/2$

1. $m$ $m$ $>$ $>$ $5$ $5$
2. $m$ $m$ $<$ $<$ $- 5$ $-5$
3. $m$ $m$ $>$ $>$ $- 5$ $-5$
4. $m$ $m$ $<$ $<$ $5$ $5$

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

- x

$-x$

<

$<$

a

$a$ becomes

x

$x$

>

$>$

- a

$-a$

First, make sure that only

m

$m$ is on the left side

$\frac{m}{10}$ $m/10$	$>$ $>$	$\frac{1}{2}$ $1/2$

$- \frac{m}{10}$ $-m/10$ $\times 10$ $times10$	$>$ $>$	$\frac{1}{2}$ $1/2$ $\times 10$ $times10$	Multiply both sides by $10$ $10$

$- m$ $-m$	$>$ $>$	$\frac{10}{2}$ $10/2$	$\frac{10}{10} = 1$ $10/10=1$

$- m$ $-m$ $\times (- 1)$ $times(-1)$	$>$ $>$	$5$ $5$ $\times (- 1)$ $times(-1)$	Multiply both sides by $- 1$ $-1$
$m$ $m$	$<$ $<$	$- 5$ $-5$	Flip the inequality

m

$m$

<

$<$

- 5

$-5$

Question 3 of 3

Find the inequality that represents all possible

t

$t$ values

\frac{3 t}{8}

$(3t)/8$

<

$<$

- \frac{5}{40}

$-5/40$

1. $t$ $t$ $<$ $<$ $\frac{1}{3}$ $1/3$
2. $t$ $t$ $>$ $>$ $\frac{1}{3}$ $1/3$
3. $t$ $t$ $<$ $<$ $- \frac{1}{3}$ $-1/3$
4. $t$ $t$ $>$ $>$ $- \frac{1}{3}$ $-1/3$

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

- x

$-x$

<

$<$

a

$a$ becomes

x

$x$

>

$>$

- a

$-a$

First, make sure that only

m

$m$ is on the left side

$\frac{3 t}{8}$ $(3t)/8$	$<$ $<$	$- \frac{5}{40}$ $-5/40$

$\frac{3 t}{8}$ $(3t)/8$ $\times \frac{8}{3}$ $times8/3$	$<$ $<$	$- \frac{5}{40}$ $-5/40$ $\times \frac{8}{3}$ $times8/3$	Multiply both sides by $\frac{8}{3}$ $8/3$

$t$ $t$	$<$ $<$	$- \frac{40}{120}$ $-40/120$	$\frac{8 \times 3}{8 \times 3} = 1$ $(8times3)/(8times3)=1$

$t$ $t$	$<$ $<$	$- \frac{1}{3}$ $-1/3$	Simplify

t

$t$

<

$<$

- \frac{1}{3}

$-1/3$

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Quiz summary

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1. Question

Hint

Excellent!

Representing Inequalities in the Number Line

2. Question

Hint

Nice Job!

3. Question

Hint

Well Done!

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