Using properties of equalities, find the solution to the equation 3/7x+6/7−2x=4

Question

.(1 point)
Responses

−2
negative 2

−22
negative 22

22
22

2

Answer 1

To solve the equation \(\frac{3}{7}x + \frac{6}{7} - 2x = 4\), we can follow these steps:

1. Combine like terms: First, rewrite \(2x\) as \(\frac{14}{7}x\) so that we can combine it with \(\frac{3}{7}x\).

   \[ \frac{3}{7}x - \frac{14}{7}x + \frac{6}{7} = 4 \]

   This simplifies to:

   \[ \frac{3 - 14}{7}x + \frac{6}{7} = 4 \]

   \[ -\frac{11}{7}x + \frac{6}{7} = 4 \]

2. Isolate the \(x\) term: Subtract \(\frac{6}{7}\) from both sides.

   \[ -\frac{11}{7}x = 4 - \frac{6}{7} \]

   Convert \(4\) to a fraction with a denominator of \(7\):

   \[ 4 = \frac{28}{7} \]

   So,

   \[ 4 - \frac{6}{7} = \frac{28}{7} - \frac{6}{7} = \frac{22}{7} \]

   Therefore, we have:

   \[ -\frac{11}{7}x = \frac{22}{7} \]

3. Solve for \(x\): To isolate \(x\), we can multiply both sides by \(-\frac{7}{11}\):

   \[ x = \frac{22}{7} \cdot -\frac{7}{11} \]

   The \(\frac{7}{7}\) cancels out:

   \[ x = -\frac{22}{11} = -2 \]

Thus, the solution to the equation is:

\(\boxed{-2}\)