Let's solve the equation \( \frac{X}{7} + 5 = \frac{27}{42} \).

### Step 1: Subtract 5 from both sides
To isolate the term with \( X \), subtract 5 from both sides:

\[
\frac{X}{7} = \frac{27}{42} - 5
\]

### Step 2: Simplify the right side
First, express 5 as a fraction with a denominator of 42:

\[
5 = \frac{5 \times 42}{42} = \frac{210}{42}
\]

Now subtract:

\[
\frac{X}{7} = \frac{27}{42} - \frac{210}{42} = \frac{27 - 210}{42} = \frac{-183}{42}
\]

### Step 3: Multiply both sides by 7
To solve for \( X \), multiply both sides by 7:

\[
X = 7 \times \frac{-183}{42}
\]

### Step 4: Simplify the expression
Simplify the multiplication:

\[
X = \frac{-1281}{42} = -30.5
\]

So, the solution is \( X = -30.5 \).

Would you like more details or have any other questions?

### Related Questions
1. How can you solve equations with variables on both sides?
2. What is the process of simplifying fractions?
3. How do you convert a mixed number to an improper fraction?
4. How does changing the denominator affect fraction addition or subtraction?
5. Can equations with fractions always be simplified?

### Tip
When dealing with equations that include fractions, it's often helpful to eliminate the fractions early by multiplying through by the common denominator.

Learn how to solve the equation X/7 + 5 = 27/42 with a detailed step-by-step solution. This problem explores algebraic concepts like solving equations with fractions and simplifying fractions. Suitable for students in Grades 6-8.

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