Solve for xx. Express your answer as a proper or improper fraction in simplest terms.
start fraction, 4, divided by, 11, end fraction, x, plus, one quarter, equals, one eigth
11
4
​
x+
4
1
​
=
8
1
​

We are given the equation:

\[
\frac{4}{11}x + \frac{1}{4} = \frac{1}{8}
\]

To solve for \( x \), follow these steps:

### Step 1: Subtract \( \frac{1}{4} \) from both sides

\[
\frac{4}{11}x = \frac{1}{8} - \frac{1}{4}
\]

### Step 2: Simplify \( \frac{1}{8} - \frac{1}{4} \)

To subtract these fractions, we need a common denominator. The least common denominator between 8 and 4 is 8. Rewrite \( \frac{1}{4} \) as \( \frac{2}{8} \):

\[
\frac{1}{8} - \frac{2}{8} = -\frac{1}{8}
\]

Now the equation becomes:

\[
\frac{4}{11}x = -\frac{1}{8}
\]

### Step 3: Solve for \( x \)

To isolate \( x \), multiply both sides by the reciprocal of \( \frac{4}{11} \), which is \( \frac{11}{4} \):

\[
x = -\frac{1}{8} \times \frac{11}{4}
\]

Multiply the numerators and denominators:

\[
x = -\frac{11}{32}
\]

Thus, the solution is:

\[
x = -\frac{11}{32}
\]

Would you like further clarification or more details?

Here are 5 related questions:
1. How do you find the least common denominator?
2. What is the process of subtracting fractions with different denominators?
3. How can you check your solution for \( x \) in the original equation?
4. What does it mean to simplify a fraction?
5. How do you multiply fractions?

**Tip:** When dealing with equations that involve fractions, it’s useful to eliminate fractions early by multiplying both sides by the least common denominator!

Solve for x. Express your answer as a proper or improper fraction in simplest terms. (4/11)x + 1/4 = 1/8

Step-by-step solution to solve the linear equation (4/11)x + 1/4 = 1/8. Learn key algebraic concepts like subtracting fractions, finding common denominators, and solving for variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solve for xx. Express your answer as a proper or improper fraction in simplest terms. start fraction, 4, divided by, 11, end fraction, x, plus, one quarter, equals, one eigth 11 4 x+ 4 1

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