One Step Inequalities 1

Years

Year 9

Inequalities

One Step Inequalities

One Step Inequalities 1

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Question 1 of 5

1. Question
Choose the number line that represents the inequality

$x - 35 \leq 14$ $x-35≤14$
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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

$x - 35$ $x-35$ $\leq$ $≤$ $14$ $14$

$x - 35$ $x-35$ $+ 35$ $+35$ $\leq$ $≤$ $14$ $14$ $+ 35$ $+35$ Add $35$ $35$ to both sides

$x$ $x$ $\leq$ $≤$ $49$ $49$

The given inequality has a less than or equal to ( $\leq$ $≤$ ) sign.

Hence, place a solid circle above $49$ $49$ and attach an arrow pointing to the left to represent all values less than $49$ $49$ .

Check our work

To confirm that $49$ $49$ is less than or equal to $a$ $a$ , substitute $x = 49$ $x=49$ to the original inequality

$x - 35$ $x-35$ $\leq$ $≤$ $14$ $14$

$49 - 35$ $49-35$ $\leq$ $≤$ $14$ $14$ Substitute $x = 49$ $x=49$

$14$ $14$ $\leq$ $≤$ $14$ $14$

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

2. Question
Choose the number line that represents the inequality

$9$ $9$ $<$ $<$ $m + 3$ $m+3$
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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

$9$ $9$ $<$ $<$ $m + 3$ $m+3$

$9$ $9$ $- 3$ $-3$ $<$ $<$ $m + 3$ $m+3$ $- 3$ $-3$ Subtract $3$ $3$ from both sides

$6$ $6$ $<$ $<$ $m$ $m$

$m$ $m$ $>$ $>$ $6$ $6$ Flip the inequality

The given inequality has a greater than ( $>$ $>$ ) sign.

Hence, place an empty circle above $6$ $6$ and attach an arrow pointing to the right to represent all values greater than $6$ $6$ .
Question 3 of 5

3. Question
Choose the number line that represents the inequality

$8 x + 5$ $8x+5$ $>$ $>$ $9 x$ $9x$
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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

$8 x + 5$ $8x+5$ $>$ $>$ $9 x$ $9x$

$8 x + 5$ $8x+5$ $- 8 x$ $-8x$ $>$ $>$ $9 x$ $9x$ $- 8 x$ $-8x$ Subtract $8 x$ $8x$ from both sides

$5$ $5$ $>$ $>$ $x$ $x$

$x$ $x$ $<$ $<$ $5$ $5$ Flip the inequality

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

Hence, place an empty circle above $5$ $5$ and attach an arrow pointing to the left to represent all values less than $5$ $5$ .

Question 4 of 5

Choose the number line that represents the inequality

a + 15.8 \geq - 3.5

$a+15.8≥-3.5$

Question 5 of 5

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

$- 3 a$ $-3a$ $<$ $<$ $45$ $45$
- 1. $a$ $a$ $>$ $>$ $- 15$ $-15$
- 2. $a$ $a$ $<$ $<$ $- 15$ $-15$
- 3. $a$ $a$ $<$ $<$ $15$ $15$
- 4. $a$ $a$ $>$ $>$ $15$ $15$
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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

$- 3 a$ $-3a$ $<$ $<$ $45$ $45$

$- 3 a$ $-3a$ $\div (- 3)$ $divide(-3)$ $<$ $<$ $45$ $45$ $\div (- 3)$ $divide(-3)$ Divide both sides by $- 3$ $-3$

$a$ $a$ $>$ $>$ $- 15$ $-15$ Flip the inequality

$a$ $a$ $>$ $>$ $- 15$ $-15$

$a + 15.8$ $a+15.8$	$\geq$ $≥$	$- 3.5$ $-3.5$

$a + 15.8$ $a+15.8$ $- 15.8$ $-15.8$	$\geq$ $≥$	$- 3.5$ $-3.5$ $- 15.8$ $-15.8$	Subtract $15.8$ $15.8$ from both sides
$a$ $a$	$\geq$ $≥$	$- 19.3$ $-19.3$

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Quiz summary

Information

1. Question

Hint

Correct!

Representing Inequalities in the Number Line

2. Question

Hint

Great Work!

Representing Inequalities in the Number Line

3. Question

Hint

Well Done!

Representing Inequalities in the Number Line

4. Question

Hint

Excellent!

Representing Inequalities in the Number Line

5. Question

Hint

Keep Going!

Quizzes

$x - 35$ $x-35$	$\leq$ $≤$	$14$ $14$

$x - 35$ $x-35$ $+ 35$ $+35$	$\leq$ $≤$	$14$ $14$ $+ 35$ $+35$	Add $35$ $35$ to both sides

$x$ $x$	$\leq$ $≤$	$49$ $49$

$9$ $9$	$<$ $<$	$m + 3$ $m+3$

$9$ $9$ $- 3$ $-3$	$<$ $<$	$m + 3$ $m+3$ $- 3$ $-3$	Subtract $3$ $3$ from both sides

$6$ $6$	$<$ $<$	$m$ $m$
$m$ $m$	$>$ $>$	$6$ $6$	Flip the inequality

$8 x + 5$ $8x+5$	$>$ $>$	$9 x$ $9x$

$8 x + 5$ $8x+5$ $- 8 x$ $-8x$	$>$ $>$	$9 x$ $9x$ $- 8 x$ $-8x$	Subtract $8 x$ $8x$ from both sides

$5$ $5$	$>$ $>$	$x$ $x$
$x$ $x$	$<$ $<$	$5$ $5$	Flip the inequality

$- 3 a$ $-3a$	$<$ $<$	$45$ $45$
$- 3 a$ $-3a$ $\div (- 3)$ $divide(-3)$	$<$ $<$	$45$ $45$ $\div (- 3)$ $divide(-3)$	Divide both sides by $- 3$ $-3$
$a$ $a$	$>$ $>$	$- 15$ $-15$	Flip the inequality