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Solving Addition Equations

Try to solve as many of the following equations in your head as you can.

**Example:**
[tex]\[ X + 25 = 100 \][/tex]
What number plus 25 equals 100? Since [tex]\( 75 + 25 = 100 \)[/tex], then [tex]\( X = 75 \)[/tex].

To solve the equations, you can also use the opposite operation on both sides. This balances the equation and gives you the answer.

[tex]\[
\begin{align*}
X + 25 &= 100 \\
X + 25 - 25 &= 100 - 25 \\
100 - 25 &= 75 \quad \text{so} \quad X = 75 \\
\end{align*}
\][/tex]

Always fit your answer back in to check.
Since [tex]\( 75 + 25 = 100 \)[/tex], 75 is the correct answer.

**Solve each equation:**

[tex]\[
\begin{array}{|l|l|l|}
\hline
1. \; m + 60 = 110 & 2. \; c + 30 = 130 & 3. \; 81 = 11 + b \\
\hline
4. \; x + 27 = 48 & 5. \; n + 15 = 100 & 6. \; n + 22 = 75 \\
\hline
\end{array}
\][/tex]

Answer :

Sure! Let's solve each of these addition equations step-by-step.

1. Equation: [tex]\( m + 60 = 110 \)[/tex]
- To find the value of [tex]\( m \)[/tex], subtract 60 from both sides of the equation:
[tex]\[ m = 110 - 60 \][/tex]
- So, [tex]\( m = 50 \)[/tex].

2. Equation: [tex]\( c + 30 = 130 \)[/tex]
- To find the value of [tex]\( c \)[/tex], subtract 30 from both sides:
[tex]\[ c = 130 - 30 \][/tex]
- So, [tex]\( c = 100 \)[/tex].

3. Equation: [tex]\( 81 = 11 + b \)[/tex]
- To find the value of [tex]\( b \)[/tex], subtract 11 from both sides:
[tex]\[ b = 81 - 11 \][/tex]
- So, [tex]\( b = 70 \)[/tex].

4. Equation: [tex]\( x + 27 = 48 \)[/tex]
- To find the value of [tex]\( x \)[/tex], subtract 27 from both sides:
[tex]\[ x = 48 - 27 \][/tex]
- So, [tex]\( x = 21 \)[/tex].

5. Equation: [tex]\( n + 15 = 100 \)[/tex]
- To find the value of [tex]\( n \)[/tex], subtract 15 from both sides:
[tex]\[ n = 100 - 15 \][/tex]
- So, [tex]\( n = 85 \)[/tex].

6. Equation: [tex]\( n + 22 = 75 \)[/tex]
- To find the value of [tex]\( n \)[/tex], subtract 22 from both sides:
[tex]\[ n = 75 - 22 \][/tex]
- So, [tex]\( n = 53 \)[/tex].

These are the values for each variable based on the given equations:
- [tex]\( m = 50 \)[/tex]
- [tex]\( c = 100 \)[/tex]
- [tex]\( b = 70 \)[/tex]
- [tex]\( x = 21 \)[/tex]
- [tex]\( n = 85 \)[/tex] (for the equation [tex]\( n + 15 = 100 \)[/tex])
- [tex]\( n = 53 \)[/tex] (for the equation [tex]\( n + 22 = 75 \)[/tex])

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