Question

Solve the following linear equation.





47x+10=−8\frac{4}{7}x+10=-8
7
4
​
x+10=−8



x=x=x=

Answer 1

To solve the equation \( 47x + 10 = -8 \frac{4}{7} x + 10 \), we first need to convert the mixed number \(-8 \frac{4}{7}\) into an improper fraction.

- The mixed number \(-8 \frac{4}{7}\) can be expressed as:

\[
-8 \frac{4}{7} = -\left(8 + \frac{4}{7}\right) = -\left(\frac{56}{7} + \frac{4}{7}\right) = -\frac{60}{7}
\]

Now we can rewrite the equation:

\[
47x + 10 = -\frac{60}{7} x + 10
\]

Next, we will subtract 10 from both sides:

\[
47x = -\frac{60}{7} x
\]

Now let's get all terms involving \(x\) on one side:

\[
47x + \frac{60}{7} x = 0
\]

To combine the terms, we need a common denominator. The common denominator of 1 (for \(47x\)) and 7 (for \(\frac{60}{7} x\)) is 7. We can express \(47x\) with the common denominator:

\[
47x = \frac{47 \cdot 7}{7} x = \frac{329}{7} x
\]

Now substitute it back into the equation:

\[
\frac{329}{7} x + \frac{60}{7} x = 0
\]

Combining the two fractions gives:

\[
\frac{329 + 60}{7} x = 0
\]

\[
\frac{389}{7} x = 0
\]

To isolate \(x\), we multiply both sides by \(\frac{7}{389}\):

\[
x = 0
\]

Thus, the solution to the equation is:

\[
\boxed{0}
\]