Solve for
x
x
:

1
4
x
+
1
3
=
4
1
4
x
+
1
3
=
4

You can enter your answer as an improper fraction (like 13/4), but not as a mixed number.

The given equation is:

\[
\frac{1}{4}x + \frac{1}{3} = 4
\]

### Step 1: Isolate the variable term
First, subtract \(\frac{1}{3}\) from both sides to isolate the term involving \(x\).

\[
\frac{1}{4}x = 4 - \frac{1}{3}
\]

To simplify \(4 - \frac{1}{3}\), we need to express 4 as a fraction with the same denominator as \(\frac{1}{3}\). We write 4 as \(\frac{12}{3}\), so:

\[
4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{11}{3}
\]

Now the equation becomes:

\[
\frac{1}{4}x = \frac{11}{3}
\]

### Step 2: Solve for \(x\)
To solve for \(x\), multiply both sides by 4 to eliminate the fraction on the left-hand side.

\[
x = 4 \times \frac{11}{3}
\]

Multiply:

\[
x = \frac{44}{3}
\]

### Final Answer:
\[
x = \frac{44}{3}
\]

Would you like any further details or explanations on this solution?

Here are 5 related questions to deepen your understanding:
1. What happens if you multiply both sides of an equation by a common denominator first?
2. How do you convert a mixed number to an improper fraction?
3. What is the process of solving equations with fractions in general?
4. How do you simplify fractions when solving for a variable?
5. Can this equation be solved using cross-multiplication?

**Tip:** When solving equations involving fractions, a helpful approach is to find a common denominator to simplify the equation early on.

Solve for x: (1/4)x + 1/3 = 4. You can enter your answer as an improper fraction (like 13/4), but not as a mixed number.

Learn how to solve the linear equation (1/4)x + 1/3 = 4, with a step-by-step guide using fraction manipulation. This problem highlights important algebraic concepts such as isolating the variable, finding common denominators, and solving linear equations with fractions. Ideal for Grades 6-8.

Math Problem Statement

1 4 x + 1 3

4 1 4 x + 1 3

Solution

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