Multi-Step Inequalities 2

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Question 1 of 4

Find the inequality that represents all possible

$a$ values

$a+7≥3a-4$

1. $a≤5 1/2$
2. $a≥5 1/2$
3. $a≤-5 1/2$
4. $a≥-5 1/2$

Question 2 of 4

2. Question
Choose the number line that represents the inequality

$-7(y+2)+8y$ $<$ $-14$
- 1.
- 2.
- 3.
- 4.
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Representing Inequalities in the Number Line

Greater than ( $>$ )

Greater than or equal ( $≥$ )

Less than ( $<$ )

Less than or equal ( $≤$ )

First, make sure that only $y$ is on the left side

$-7(y+2)+8y$ $<$ $-14$

$-7y-14+8y$ $<$ $-14$ Expand

$y-14$ $<$ $-14$ Combine like terms

$y-14$ $+14$ $<$ $-14$ $+14$ Add $14$ to both sides

$y$ $<$ $0$

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

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

Question 3 of 4

Choose the number line that represents the inequality

$(x-2)/2$

$>$

$(x+1)/4$

Question 4 of 4

Simplify

$(3x)/5+2≤(2x)/5$

1. $x≥-10$
2. $x≤10$
3. $x≤-10$
4. $x≥10$

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

$a$	$≤$	$5 1/2$	Flip the inequality

$(x-2)/2$	$>$	$(x+1)/4$

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

$(3x)/5+2$	$≤$	$(2x)/5$

$((3x)/5+2)$ $times5$	$≤$	$((2x)/5)$ $times5$	Multiply both sides by $5$

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

Multi-Step Inequalities 2

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Quiz summary

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1. Question

Hint

Great Work!

2. Question

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Fantastic!

Representing Inequalities in the Number Line

3. Question

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Well Done!

Representing Inequalities in the Number Line

4. Question

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Fantastic!

Representing Inequalities in the Number Line

Quizzes

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