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------------------------------------------------ 9.1: Math Talk: Opposites Attract

Solve each equation mentally.

1. [tex]40 - 8 = 40 + n[/tex]

2. [tex]25 + (-100) = 25 - n[/tex]

3. [tex]3 - \frac{1}{2} = 3 + n[/tex]

4. [tex]72 - n = 72 + 6[/tex]

Sure! Let's solve each equation step by step:

1. Equation 1: [tex]\(40 - 8 = 40 + n\)[/tex]

- Simplify the left side: [tex]\(40 - 8 = 32\)[/tex].
- So the equation becomes: [tex]\(32 = 40 + n\)[/tex].
- To solve for [tex]\(n\)[/tex], subtract 40 from both sides:
[tex]\[
32 - 40 = n \\
-8 = n
\][/tex]
- So, [tex]\(n = -8\)[/tex].

2. Equation 2: [tex]\(25 + (-100) = 25 - n\)[/tex]

- Simplify the left side: [tex]\(25 - 100 = -75\)[/tex].
- So the equation becomes: [tex]\(-75 = 25 - n\)[/tex].
- To solve for [tex]\(n\)[/tex], add [tex]\(n\)[/tex] to both sides and then add 75 to both sides:
[tex]\[
n = 25 + 75 \\
n = 100
\][/tex]
- So, [tex]\(n = 100\)[/tex].

3. Equation 3: [tex]\(3 - \frac{1}{2} = 3 + n\)[/tex]

- Simplify the left side: [tex]\(3 - \frac{1}{2} = 2.5\)[/tex].
- So the equation becomes: [tex]\(2.5 = 3 + n\)[/tex].
- To solve for [tex]\(n\)[/tex], subtract 3 from both sides:
[tex]\[
2.5 - 3 = n \\
-0.5 = n
\][/tex]
- So, [tex]\(n = -0.5\)[/tex].

4. Equation 4: [tex]\(72 - n = 72 + 6\)[/tex]

- Simplify the right side: [tex]\(72 + 6 = 78\)[/tex].
- So the equation becomes: [tex]\(72 - n = 78\)[/tex].
- To solve for [tex]\(n\)[/tex], subtract 72 from both sides and then multiply by -1:
[tex]\[
-n = 78 - 72 \\
-n = 6 \\
n = -6
\][/tex]
- So, [tex]\(n = -6\)[/tex].

Therefore, the solutions are:
1. [tex]\(n = -8\)[/tex]
2. [tex]\(n = 100\)[/tex]
3. [tex]\(n = -0.5\)[/tex]
4. [tex]\(n = -6\)[/tex]