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Solving linear equations is a fundamental skill in algebra. A linear equation is a statement of equality between two expressions. When we solve these equations, we are looking for the value of the variable that makes the equation true.

The given equation is \(\frac{a}{4} = 13\). This means that some number divided by 4 equals 13. To solve for the variable, we need to perform operations that will isolate the variable on one side of the equation.

Linear equations can involve various operations such as addition, subtraction, multiplication, or division. The goal is always to isolate the variable in the equation. The multiplication principle helps in situations where the variable is being divided by a number, as seen in our exercise.

Isolating the variable is a critical step in solving linear equations. This means getting the variable by itself on one side of the equation.

In our exercise, the initial equation is \(\frac{a}{4} = 13\). Since the variable \(a\) is divided by 4, we can isolate \(a\) by performing the inverse operation of division, which is multiplication.

• Step 1: Multiply both sides of the equation by 4, like this: 4 \( \times \frac{a}{4} = 13 \times 4 \)
• Step 2: Simplify both sides:
• On the left side, 4 \( \times \frac{a}{4}\) simplifies to just \(a\) because \( 4 \times /\frac{4}= 1 \), so we have \(a \). On the right side, 13 \times 4 = 52.
  
• Result: After simplification, the equation becomes \( a = 52 \). This is the solution.

Verifying solutions is essential to ensure the accuracy of your answer. After finding the value of the variable that you believe solves the equation, substitute it back into the original equation to see if both sides are equal.

Let's verify our solution \(a = 52\).

• Substitute \(52\) into \(\frac{a}{4} = 13\):
• We get \(\frac{52}{4}\).
• Simplify the left side: \( \frac{52}{4} = 13\), which means both sides are equal.

Since \(13\) equals \(13\), our solution \(a = 52\) is correct. Always remember to check your work to prevent any errors.

By following these steps diligently, you will consistently solve linear equations accurately. Happy solving!