Sure, let's walk through the solutions for each of the equations step-by-step and justify each step.
### 1) [tex]\( 10 = 7 - m \)[/tex]
First, we want to isolate [tex]\( m \)[/tex].
1. Subtract 7 from both sides to get:
[tex]\[
10 - 7 = -m
\][/tex]
Simplifying the left side, we have:
[tex]\[
3 = -m
\][/tex]
2. To solve for [tex]\( m \)[/tex], multiply both sides by -1:
[tex]\[
m = -3
\][/tex]
### 2) [tex]\( \frac{h + 6}{5} = 2 \)[/tex]
To solve for [tex]\( h \)[/tex], we need to eliminate the fraction:
1. Multiply both sides by 5:
[tex]\[
h + 6 = 10
\][/tex]
2. Subtract 6 from both sides:
[tex]\[
h = 10 - 6
\][/tex]
3. Simplify the right side:
[tex]\[
h = 4
\][/tex]
### 3) [tex]\( 36 = 13n - 4n \)[/tex]
To solve for [tex]\( n \)[/tex], first combine like terms on the right side of the equation:
1. Combine terms involving [tex]\( n \)[/tex]:
[tex]\[
36 = (13 - 4)n
\][/tex]
This simplifies to:
[tex]\[
36 = 9n
\][/tex]
2. Divide both sides by 9:
[tex]\[
n = \frac{36}{9}
\][/tex]
3. Simplify the right side:
[tex]\[
n = 4
\][/tex]
### 4) [tex]\( -2(4g - 3) = 30 \)[/tex]
To isolate [tex]\( g \)[/tex], we use the distributive property first and then solve for [tex]\( g \)[/tex]:
1. Apply the distributive property:
[tex]\[
-8g + 6 = 30
\][/tex]
2. Subtract 6 from both sides:
[tex]\[
-8g = 30 - 6
\][/tex]
Simplifying the right side, we have:
[tex]\[
-8g = 24
\][/tex]
3. Divide both sides by -8:
[tex]\[
g = \frac{24}{-8}
\][/tex]
4. Simplify the right side:
[tex]\[
g = -3
\][/tex]
So, the solutions for the equations are:
1. [tex]\( m = -3 \)[/tex]
2. [tex]\( h = 4 \)[/tex]
3. [tex]\( n = 4 \)[/tex]
4. [tex]\( g = -3 \)[/tex]
