One Step Inequalities 2

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Algebra 1

Inequalities

One Step Inequalities

One Step Inequalities 2

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Question 1 of 5

1. Question
Choose the number line that represents the inequality

$\frac{a}{5} \geq 19$ $a/5≥19$
- 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 $a$ $a$ is on the left side

$\frac{a}{5}$ $a/5$ $\geq$ $≥$ $19$ $19$

$\frac{a}{5}$ $a/5$ $\times 5$ $times5$ $\geq$ $≥$ $19$ $19$ $\times 5$ $times5$ Multiply both sides by $5$ $5$

$a$ $a$ $\geq$ $≥$ $95$ $95$

The given inequality has a greater than or equal to ( $\geq$ $≥$ ) sign.

Hence, place a solid circle above $95$ $95$ and attach an arrow pointing to the right to represent all values greater than $95$ $95$ .

Check our work

To confirm that $95$ $95$ is greater than or equal to $a$ $a$ , substitute $a = 100$ $a=100$ to the original inequality

$\frac{a}{5}$ $a/5$ $\geq$ $≥$ $19$ $19$

$\frac{100}{5}$ $100/5$ $\geq$ $≥$ $19$ $19$ Substitute $a = 100$ $a=100$

$20$ $20$ $\geq$ $≥$ $19$ $19$

Since the inequality is true, the representation is correct
Question 2 of 5

2. Question
Choose the number line that represents the inequality

$\frac{x}{- 4}$ $x/(-4)$ $>$ $>$ $9$ $9$
- 1.
- 2.
- 3.
- 4.
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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 $a$ $a$ is on the left side

$\frac{x}{- 4}$ $x/(-4)$ $>$ $>$ $9$ $9$

$\frac{x}{- 4}$ $x/(-4)$ $\times (- 4)$ $times(-4)$ $>$ $>$ $9$ $9$ $\times (- 4)$ $times(-4)$ Multiply both sides by $- 4$ $-4$

$x$ $x$ $<$ $<$ $- 36$ $-36$ Flip the inequality

The given inequality has a less than ( $<$ $<$ ) sign.

Hence, place an empty circle above $- 36$ $-36$ and attach an arrow pointing to the left to represent all values less than $- 36$ $-36$ .

Question 3 of 5

Find the inequality that represents all possible

y

$y$ values

- 0.9 y

$-0.9y$

>

$>$

8.1

$8.1$

1. $y$ $y$ $<$ $<$ $- 9$ $-9$
2. $y$ $y$ $>$ $>$ $- 9$ $-9$
3. $y$ $y$ $<$ $<$ $9$ $9$
4. $y$ $y$ $>$ $>$ $9$ $9$

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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

y

$y$ is on the left side

$- 0.9 y$ $-0.9y$	$>$ $>$	$8.1$ $8.1$
$- 0.9 y$ $-0.9y$ $\div (- 0.9)$ $divide(-0.9)$	$>$ $>$	$8.1$ $8.1$ $\div (- 0.9)$ $divide(-0.9)$	Divide both sides by $- 0.9$ $-0.9$
$y$ $y$	$<$ $<$	$- 9$ $-9$	Flip the inequality

y

$y$

<

$<$

- 9

$-9$

Question 4 of 5

4. Question
Find the inequality that represents all possible $x$ $x$ values

$- \frac{1}{2} x$ $-1/2x$ $<$ $<$ $- 24$ $-24$
- 1. $x$ $x$ $<$ $<$ $48$ $48$
- 2. $x$ $x$ $>$ $>$ $48$ $48$
- 3. $x$ $x$ $>$ $>$ $- 48$ $-48$
- 4. $x$ $x$ $<$ $<$ $- 48$ $-48$
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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 $y$ $y$ is on the left side

$- \frac{1}{2} x$ $-1/2x$ $<$ $<$ $- 24$ $-24$

$- \frac{1}{2} x$ $-1/2x$ $\times (- 2)$ $times(-2)$ $<$ $<$ $- 24$ $-24$ $\times (- 2)$ $times(-2)$ Multiply both sides by $- 2$ $-2$

$x$ $x$ $>$ $>$ $48$ $48$ Flip the inequality

$x$ $x$ $>$ $>$ $48$ $48$
Question 5 of 5

5. Question
Find the inequality that represents all possible $t$ $t$ values

$- 6 t \leq 222$ $-6t≤222$
- 1. $t \leq 37$ $t≤37$
- 2. $t \geq 37$ $t≥37$
- 3. $t \leq - 37$ $t≤-37$
- 4. $t \geq - 37$ $t≥-37$
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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 $y$ $y$ is on the left side

$- 6 t$ $-6t$ $\leq$ $≤$ $222$ $222$

$- 6 t$ $-6t$ $\div (- 6)$ $divide(-6)$ $\leq$ $≤$ $222$ $222$ $\div (- 6)$ $divide(-6)$ Divide both sides by $- 6$ $-6$

$t$ $t$ $\geq$ $≥$ $- 37$ $-37$ Flip the inequality

$t \geq - 37$ $t≥-37$

One Step Inequalities 2

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Quiz summary

Information

1. Question

Hint

Great Work!

Representing Inequalities in the Number Line

2. Question

Hint

Nice Job!

3. Question

Hint

Fantastic!

4. Question

Hint

Correct!

5. Question

Hint

Exceptional!

Quizzes

$\frac{a}{5}$ $a/5$	$\geq$ $≥$	$19$ $19$

$\frac{a}{5}$ $a/5$ $\times 5$ $times5$	$\geq$ $≥$	$19$ $19$ $\times 5$ $times5$	Multiply both sides by $5$ $5$

$a$ $a$	$\geq$ $≥$	$95$ $95$

$\frac{x}{- 4}$ $x/(-4)$	$>$ $>$	$9$ $9$

$\frac{x}{- 4}$ $x/(-4)$ $\times (- 4)$ $times(-4)$	$>$ $>$	$9$ $9$ $\times (- 4)$ $times(-4)$	Multiply both sides by $- 4$ $-4$

$x$ $x$	$<$ $<$	$- 36$ $-36$	Flip the inequality

$- \frac{1}{2} x$ $-1/2x$	$<$ $<$	$- 24$ $-24$

$- \frac{1}{2} x$ $-1/2x$ $\times (- 2)$ $times(-2)$	$<$ $<$	$- 24$ $-24$ $\times (- 2)$ $times(-2)$	Multiply both sides by $- 2$ $-2$

$x$ $x$	$>$ $>$	$48$ $48$	Flip the inequality

$- 6 t$ $-6t$	$\leq$ $≤$	$222$ $222$
$- 6 t$ $-6t$ $\div (- 6)$ $divide(-6)$	$\leq$ $≤$	$222$ $222$ $\div (- 6)$ $divide(-6)$	Divide both sides by $- 6$ $-6$
$t$ $t$	$\geq$ $≥$	$- 37$ $-37$	Flip the inequality