Question

Solve the following linear equation. Click Here for Help Video





27x+8=−2\frac{2}{7}x+8=-2
7
2
​
x+8=−2



x =x\ =x =

Answer 1

To solve the equation \(27x + 8 = -2\frac{2}{7}x + 8\), we first need to convert the mixed number \(-2\frac{2}{7}\) into an improper fraction.

\[
-2\frac{2}{7} = -\left(2 \times 7 + 2\right)/7 = -\frac{14 + 2}{7} = -\frac{16}{7}
\]

Now we can rewrite the equation as:

\[
27x + 8 = -\frac{16}{7}x + 8
\]

Next, we'll eliminate the \(8\) from both sides of the equation:

\[
27x = -\frac{16}{7}x
\]

Now, let's isolate \(x\). To do this, we can add \(\frac{16}{7}x\) to both sides:

\[
27x + \frac{16}{7}x = 0
\]

To combine these two terms, we need a common denominator. The common denominator between \(27\) and \(7\) is \(189\). Rewriting \(27x\) with this common denominator gives:

\[
27x = \frac{27 \times 7}{7}x = \frac{189}{7}x
\]

Now we have:

\[
\frac{189}{7}x + \frac{16}{7}x = 0
\]

Combine the left-hand side:

\[
\frac{189 + 16}{7}x = 0 \implies \frac{205}{7}x = 0
\]

Now, for the equation to hold true, since \(\frac{205}{7} \neq 0\), we need:

\[
x = 0
\]

Thus, the solution to the equation \(27x + 8 = -2\frac{2}{7}x + 8\) is:

\[
\boxed{0}
\]