Question

Solve for xx and write your answer in simplest form.
minus, left parenthesis, 9, x, minus, one half, right parenthesis, plus, 8, x, equals, minus, start fraction, 3, divided by, 5, end fraction
−(9x−
2
1
​
)+8x=
−
5
3
​

Answer 1

Let's solve the equation step by step:

Starting with:

\[
-(9x - \frac{1}{2}) + 8x = -\frac{3}{5}
\]

First, distribute the negative sign:

\[
-9x + \frac{1}{2} + 8x = -\frac{3}{5}
\]

Now, combine like terms on the left side:

\[
(-9x + 8x) + \frac{1}{2} = -\frac{3}{5}
\]
\[
-x + \frac{1}{2} = -\frac{3}{5}
\]

Next, isolate \(-x\) by subtracting \(\frac{1}{2}\) from both sides:

\[
-x = -\frac{3}{5} - \frac{1}{2}
\]

To combine the fractions on the right side, find a common denominator. The least common multiple of 5 and 2 is 10.

Convert each fraction:

\[
-\frac{3}{5} = -\frac{6}{10}
\]
\[
-\frac{1}{2} = -\frac{5}{10}
\]

Now, combine them:

\[
-x = -\frac{6}{10} - \frac{5}{10} = -\frac{11}{10}
\]

Now, multiply both sides by -1 to solve for \(x\):

\[
x = \frac{11}{10}
\]

Thus, the solution in simplest form is:

\[
\boxed{\frac{11}{10}}
\]