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

Question

.(1 point)
Responses

2
2

22
22

−22
negative 22

−2

Answer 1

To solve the equation \( \frac{3}{7}x + \frac{6}{7} - 2x = 4 \), we can start by eliminating the fractions.

1. Combine the terms involving \( x \): \[ \frac{3}{7}x - 2x + \frac{6}{7} = 4. \] Since \( 2x \) is the same as \( \frac{14}{7}x \), we can rewrite the equation: \[ \frac{3}{7}x - \frac{14}{7}x + \frac{6}{7} = 4. \] Now, combine the \( x \) terms: \[ \frac{3 - 14}{7}x + \frac{6}{7} = 4, \] which simplifies to: \[ -\frac{11}{7}x + \frac{6}{7} = 4. \]

2. To eliminate the fraction, multiply the entire equation by 7: \[ -11x + 6 = 28. \]

3. Now, isolate the \( x \) term by subtracting 6 from both sides: \[ -11x = 28 - 6, \] which simplifies to: \[ -11x = 22. \]

4. Finally, divide both sides by -11: \[ x = \frac{22}{-11} = -2. \]

Thus, the solution to the equation is \( \boxed{-2} \).