Solve the equation and check the solution. $$\frac { 3 x - 1 } { 6 } - \frac { x + 3 } { 2 } = \frac { 3 x + 1 } { 3 }$$
A)- 2
B)4
C)3
D)- 3
E)no solution

Question

Quizplus · Accepted Answer

To solve the equation, first find a common denominator to combine the fractions. The common denominator for 6, 2, and 3 is 6. Multiply each term by 6 to eliminate the denominators:$$6 \times \frac{3x - 1}{6} - 6 \times \frac{x + 3}{2} = 6 \times \frac{3x + 1}{3}$$This simplifies to:$$3x - 1 - 3(x + 3) = 2(3x + 1)$$Expanding and simplifying:$$3x - 1 - 3x - 9 = 6x + 2$$Combine like terms:$$-10 = 6x + 2$$Subtract 2 from both sides:$$-12 = 6x$$Divide by 6:$$x = -2$$Checking the solution by substituting $x = -2$ back into the original equation:$$\frac{3(-2) - 1}{6} - \frac{(-2) + 3}{2} = \frac{3(-2) + 1}{3}$$$$\frac{-6 - 1}{6} - \frac{1}{2} = \frac{-6 + 1}{3}$$$$\frac{-7}{6} - \frac{1}{2} = \frac{-5}{3}$$Converting all terms to have a common denominator of 6:$$\frac{-7}{6} - \frac{3}{6} = \frac{-10}{6}$$$$\frac{-10}{6} = \frac{-10}{6}$$The solution checks out, so $x = -2$ is correct.

Solve the Equation and Check the Solution 3x−16−x+32=3x+13\frac { 3 x - 1 } { 6 } - \frac { x + 3 } { 2 } = \frac { 3 x + 1 } { 3 }63x−1​−2x+3​=33x+1​

Solve the Equation and Check the Solution $\frac { 3 x - 1 } { 6 } - \frac { x + 3 } { 2 } = \frac { 3 x + 1 } { 3 }$