arikatparee
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Complete all work on a separate sheet of paper. Solve the equation and justify each step.

1. [tex]10 = 7 - m[/tex]
2. [tex]\frac{h+6}{5} = 2[/tex]
3. [tex]36 = 13n - 4n[/tex]
4. [tex]-2(4g - 3) = 30[/tex]



Answer :

GinnyAnswer
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]

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