Negative Numbers with Variables 2

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Question 1 of 4

1. Question
Evaluate

$- 8 a - 5 a$ $-8a-5a$
- (-13a)
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Terms with the same variable can be added or subtracted.

Both terms have $a$ $a$ as their variable, meaning we can freely add or subtract them like integers.

Since the signs are the same $(- -)$ $(- -)$ we will find the sum of the two numbers

$8 + 5$ $8+5$ $=$ $=$ $13$ $13$ Find the Sum

$Sum$ $\text(Sum)$ $=$ $=$ $13$ $13$

Insert the sign of the larger number $(- 8)$ $(-8)$ to the difference as well as the variable $a$ $a$ .

$- 8 a - 5 a$ $-8a-5a$ $=$ $=$ $- 13 a$ $-13a$ Insert a negative sign since the larger number, $8$ $8$ is negative

$- 13 a$ $-13a$
Question 2 of 4

2. Question
Evaluate

$9 x - (- 3 x) - 16 - (- 7 x) + 24$ $9x-(-3x)-16-(-7x)+24$
- (19x+8, 8+19x)
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Terms with the same variable can be added or subtracted.

First, solve for the values with an $x$ $x$ variable.

$9 x$ $9x$ $-$ $-$ $($ $($ $-$ $-$ $3 x)$ $3x)$ $-$ $-$ $($ $($ $-$ $-$ $7 x)$ $7x)$ $=$ $=$ $9 x$ $9x$ $+$ $+$ $3 x$ $3x$ $+$ $+$ $7 x$ $7x$ Recall,

$=$ $=$ $19x$

Next, solve for the values with no variables.

Since the signs are the same $(- +)$ we will find the difference of the two numbers

$24-16$ $=$ $8$ Find the Difference

$\text(Difference)$ $=$ $8$

Insert the sign of the larger number $(+24)$ to the difference.

$-16+24$ $=$ $8$ Use a positive sign since the larger number, $24$ is positive

Finally, combine the terms.

$19x+8$

$19x+8$
Question 3 of 4

3. Question
Evaluate

$7x-(-x)-12-(+15x)+30$
- (-7x+18, 18-7x)
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Terms with the same variable can be added or subtracted.

First, solve for the values with an $x$ variable.

$7x$ $-$ $($ $-$ $x)-(+15x)$ $=$ $7x$ $+$ $x-(+15x)$ Recall,

$7x+x$ $-$ $($ $+$ $15x)$ $=$ $7x+x$ $-$ $15x$ Recall,

$=$ $8x-15x$

Since the signs are different $(+ -)$ we will find the difference of the two numbers

$15-8$ $=$ $7$ Find the Difference

$\text(Difference)$ $=$ $7$

Insert the sign of the larger number $(-15)$ to the difference as well as the variable $x$ .

$8x-15x$ $=$ $-7x$ Insert a negative sign since the larger number, $15$ is negative

Next, solve for the values with no variables.

Since the signs are different $(- +)$ we will find the difference of the two numbers

$30-12$ $=$ $18$ Find the Difference

$\text(Difference)$ $=$ $18$

Insert the sign of the larger number $(+30)$ to the difference.

$-12+30$ $=$ $18$ Use a positive sign since the larger number, $30$ is positive

Finally, combine the terms.

$-7x+18$

$-7x+18$
Question 4 of 4

4. Question
Evaluate

$-32y^3divide-8y$
- 1. $4y^2$
- 2. $4y^3$
- 3. $8y^3$
- 4. $8y^2$
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Rules for Dividing Integers

Transform the expression into a fraction to make it easier to solve.

$-32y^3divide-8y$ $=$ $(-32y^3)/(-8y)$

Simplify the fraction

$\frac{\color{#CC0000}{-32}y^3}{\color{#CC0000}{-8}y}$ $=$ $4$ $(y^3)/y$ Recall,

$=$ $4y^(3-1)$ Recall rules for indices

$=$ $4y^(2)$

$=$ $4y^2$

$4y^2$

Negative Numbers with Variables 2

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Quiz summary

Information

1. Question

Hint

Correct!

2. Question

Hint

Fantastic!

3. Question

Hint

Nice Job!

4. Question

Hint

Exceptional!

Rules for Dividing Integers

Quizzes

$8 + 5$ $8+5$	$=$ $=$	$13$ $13$	Find the Sum
$Sum$ $\text(Sum)$	$=$ $=$	$13$ $13$

$9 x$ $9x$ $-$ $-$ $($ $($ $-$ $-$ $3 x)$ $3x)$ $-$ $-$ $($ $($ $-$ $-$ $7 x)$ $7x)$	$=$ $=$	$9 x$ $9x$ $+$ $+$ $3 x$ $3x$ $+$ $+$ $7 x$ $7x$	Recall,
	$=$ $=$	$19x$

$7x$ $-$ $($ $-$ $x)-(+15x)$	$=$	$7x$ $+$ $x-(+15x)$	Recall,
$7x+x$ $-$ $($ $+$ $15x)$	$=$	$7x+x$ $-$ $15x$	Recall,
	$=$	$8x-15x$

$\frac{\color{#CC0000}{-32}y^3}{\color{#CC0000}{-8}y}$	$=$	$4$ $(y^3)/y$	Recall,

	$=$	$4y^(3-1)$	Recall rules for indices
	$=$	$4y^(2)$
	$=$	$4y^2$

$24-16$	$=$	$8$	Find the Difference
$\text(Difference)$	$=$	$8$

$15-8$	$=$	$7$	Find the Difference
$\text(Difference)$	$=$	$7$

$30-12$	$=$	$18$	Find the Difference
$\text(Difference)$	$=$	$18$