Multi-Step Inequalities 2

Topics

Algebra 1

Inequalities

Multi-Step Inequalities

Multi-Step Inequalities 2

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Question 1 of 4

Find the inequality that represents all possible

a

$a$ values

a + 7 \geq 3 a - 4

$a+7≥3a-4$

1. $a \geq - 5 \frac{1}{2}$ $a≥-5 1/2$
2. $a \leq - 5 \frac{1}{2}$ $a≤-5 1/2$
3. $a \geq 5 \frac{1}{2}$ $a≥5 1/2$
4. $a \leq 5 \frac{1}{2}$ $a≤5 1/2$

Question 2 of 4

Choose the number line that represents the inequality

- 7 (y + 2) + 8 y

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

<

$<$

- 14

$-14$

Question 3 of 4

Choose the number line that represents the inequality

\frac{x - 2}{2}

$(x-2)/2$

>

$>$

\frac{x + 1}{4}

$(x+1)/4$

Question 4 of 4

Simplify

$(3x)/5+2≤(2x)/5$

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

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

$a$ $a$	$\leq$ $≤$	$5 \frac{1}{2}$ $5 1/2$	Flip the inequality

$\frac{x - 2}{2}$ $(x-2)/2$	$>$ $>$	$\frac{x + 1}{4}$ $(x+1)/4$

$4 (x - 2)$ $4(x-2)$	$>$ $>$	$2 (x + 1)$ $2(x+1)$	Cross multiply
$4 x - 8$ $4x-8$	$>$ $>$	$2 x + 2$ $2x+2$	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

Information

1. Question

Hint

Great Work!

2. Question

Hint

Fantastic!

Representing Inequalities in the Number Line

3. Question

Hint

Well Done!

Representing Inequalities in the Number Line

4. Question

Hint

Fantastic!

Representing Inequalities in the Number Line

Quizzes

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