Solve the following equation for  
x
 :
−
4
3
−
7
8x (the x is with the 8 not next to the fraction)
=
−
7
4x (the x is with the 4 not next to the fraction)
 
Enter your answer as a simplified improper fraction, if necessary.

We are given the equation:

\[
-\frac{4}{3} - \frac{7}{8}x = -\frac{7}{4}x
\]

### Step 1: Move all terms with \( x \) to one side of the equation
To simplify the equation, let's move the \( x \)-terms to the right side by adding \(\frac{7}{8}x\) to both sides:

\[
-\frac{4}{3} = -\frac{7}{4}x + \frac{7}{8}x
\]

### Step 2: Combine like terms
Now, let's combine the \( x \)-terms on the right side. To do that, we need a common denominator for the fractions \(-\frac{7}{4}\) and \(\frac{7}{8}\). The least common denominator (LCD) is 8, so rewrite \(-\frac{7}{4}\) as:

\[
-\frac{7}{4} = -\frac{14}{8}
\]

Now the equation becomes:

\[
-\frac{4}{3} = -\frac{14}{8}x + \frac{7}{8}x
\]

Simplifying the right-hand side:

\[
-\frac{4}{3} = \left( -\frac{14}{8} + \frac{7}{8} \right)x
\]
\[
-\frac{4}{3} = -\frac{7}{8}x
\]

### Step 3: Solve for \( x \)
Now, solve for \( x \) by multiplying both sides of the equation by the reciprocal of \(-\frac{7}{8}\), which is \(-\frac{8}{7}\):

\[
x = \left( -\frac{4}{3} \right) \times \left( -\frac{8}{7} \right)
\]

Simplify the multiplication:

\[
x = \frac{4 \times 8}{3 \times 7

Solve the following equation for x: -4/3 - 7/8x = -7/4x. Enter your answer as a simplified improper fraction, if necessary.

This problem focuses on solving linear equations with fractions. Learn step-by-step how to move variables to one side, combine like terms, and use reciprocal multiplication to solve the equation -4/3 - 7/8x = -7/4x. Suitable for students in Grades 8-10.

Math Problem Statement

Solve the following equation for
x : − 4 3 − 7 8x (the x is with the 8 not next to the fraction)

Solution

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