Oksana is working to solve the equation 1

Question

3
x = −1
4
x - 10.

1. Add 1
4
x to both sides: 1
4
x + 1
3
x = −10
2. Find a common denominator: 3
12
x + 4
12
x = −10
3. Combine the terms: 7
12
x = −10
What should she do next?

Answer 1

Oksana is on the right track. After combining the terms, she has the equation:

\[ \frac{7}{12}x = -10 \]

Next, she should isolate \(x\) by multiplying both sides of the equation by the reciprocal of \(\frac{7}{12}\), which is \(\frac{12}{7}\). Here are the steps:

1. Multiply both sides by \(\frac{12}{7}\):

\[ x = -10 \cdot \frac{12}{7} \]

2. Calculate the right side:

\[ x = -\frac{120}{7} \]

Thus, the solution to the equation is:

\[ x = -\frac{120}{7} \]

If she wants to express it as a mixed number, she can convert \(-\frac{120}{7}\) to a mixed number, which would be \(-17\frac{1}{7}\).