Substitution and Evaluating Algebraic Expressions with Negative Numbers 1

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Question 1 of 4

1. Question
Evaluate $y - x$ $y-x$ using the following values:

$x = - 2$ $x=-2$

$y = - 6$ $y=-6$
- (-4)
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Rules for Adding and Subtracting Integers

Simply substitute the given value for the variable.

$x$ $x$ $=$ $=$ $- 2$ $-2$

$y$ $y$ $=$ $=$ $- 6$ $-6$

$y$ $y$ $-$ $-$ $x$ $x$ $=$ $=$ $- 6$ $-6$ $- ($ $-($ $- 2$ $-2$ $)$ $)$

$=$ $=$ $- 6 + 2$ $-6+2$

Now, we can use the number line to evaluate further.

Start at $- 6$ $-6$ , then since $2$ $2$ is positive move right $2$ $2$ places

$- 6$ $-6$ $+ 2$ $+2$ $=$ $=$

$- 6 + 2$ $-6+2$ $=$ $=$ $- 4$ $-4$

$- 4$ $-4$
Question 2 of 4

2. Question
Evaluate $y + 4 x$ $y+4x$ using the following values:

$x = - 2$ $x=-2$

$y = - 6$ $y=-6$
- (-14)
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Rules for Multiplying Integers

Simply substitute the given value for the variable.

$x$ $x$ $=$ $=$ $- 2$ $-2$

$y$ $y$ $=$ $=$ $- 6$ $-6$

$y$ $y$ $+ 4$ $+4$ $x$ $x$ $=$ $=$ $- 6$ $-6$ $+ 4 ($ $+ 4($ $- 2$ $-2$ $)$ $)$

$=$ $=$ $- 6 - 8$ $-6-8$

Now, we can use the number line to evaluate further.

Start at $- 6$ $-6$ , then subtract $8$ $8$ by moving left $8$ $8$ places

$- 6$ $-6$ $- 8$ $-8$ $=$ $=$

$- 6 - 8$ $-6-8$ $=$ $=$ $- 14$ $-14$

$- 14$ $-14$
Question 3 of 4

3. Question
Evaluate $4 m - 5 n$ $4m-5n$ using the following values:

$m = - 3$ $m=-3$

$n = - 4$ $n=-4$
- (8)
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Rules for Multiplying Integers

Simply substitute the given value for the variable.

$m$ $m$ $=$ $=$ $- 3$ $-3$

$n$ $n$ $=$ $=$ $- 4$ $-4$

$4$ $4$ $m$ $m$ $- 5$ $-5$ $n$ $n$ $=$ $=$ $4 ($ $4($ $- 3$ $-3$ $) - 5 ($ $)-5($ $- 4$ $-4$ $)$ $)$

$=$ $=$ $- 12 - 5 (- 4)$ $-12-5(-4)$

$=$ $=$ $- 12 + 20$ $-12+20$

$=$ $=$ $20 - 12$ $20-12$ Rearrange the values

$=$ $=$ $8$ $8$

$8$ $8$

Question 4 of 4

Evaluate

x^{2} y^{2}

$x^2y^2$ using the following values:

x = - 2

$x=-2$

y = - 6

$y=-6$

(144)

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Simply substitute the given value for the variable.

$x$ $x$	$=$ $=$	$- 2$ $-2$
$y$ $y$	$=$ $=$	$- 6$ $-6$

$\color{#9a00c7}{x}^2\color{#00880A}{y}^2$	$=$ $=$	$(\color{#9a00c7}{-2})^2\times(\color{#00880A}{-6})^2$

	$=$ $=$	$4 \times 36$ $4xx36$	Negative numbers raised to even exponents become positive

	$=$ $=$	$144$ $144$

144

$144$

Substitution and Evaluating Algebraic Expressions with Negative Numbers 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Rules for Adding and Subtracting Integers

2. Question

Hint

Correct!

Rules for Multiplying Integers

3. Question

Hint

Keep Going!

Rules for Multiplying Integers

4. Question

Hint

Excellent!

Quizzes

$y$ $y$ $-$ $-$ $x$ $x$	$=$ $=$	$- 6$ $-6$ $- ($ $-($ $- 2$ $-2$ $)$ $)$
	$=$ $=$	$- 6 + 2$ $-6+2$

$y$ $y$ $+ 4$ $+4$ $x$ $x$	$=$ $=$	$- 6$ $-6$ $+ 4 ($ $+ 4($ $- 2$ $-2$ $)$ $)$
	$=$ $=$	$- 6 - 8$ $-6-8$

$4$ $4$ $m$ $m$ $- 5$ $-5$ $n$ $n$	$=$ $=$	$4 ($ $4($ $- 3$ $-3$ $) - 5 ($ $)-5($ $- 4$ $-4$ $)$ $)$
	$=$ $=$	$- 12 - 5 (- 4)$ $-12-5(-4)$
	$=$ $=$	$- 12 + 20$ $-12+20$
	$=$ $=$	$20 - 12$ $20-12$	Rearrange the values
	$=$ $=$	$8$ $8$

$m$ $m$	$=$ $=$	$- 3$ $-3$
$n$ $n$	$=$ $=$	$- 4$ $-4$