Solve the equation and check the solution. $$\frac { x } { 7 } - \frac { x } { 5 } = - 6$$
A)- 105
B)105
C)210
D)- 210
E)no solution

Question

Quizplus · Accepted Answer

To solve the equation, we need to first find a common denominator for the two fractions on the left side. The least common multiple (LCM) of 7 and 5 is 35, so we can rewrite the equation as:

$$\frac{5x}{35}-\frac{7x}{35}=-6$$

Combining the two fractions, we get:

$$-\frac{2x}{35}=-6$$

Multiplying both sides by -35, we get:

$$2x=210$$

Dividing both sides by 2, we get:

$$x=105$$

To check the solution, we can substitute x=105 back into the original equation:

$$\frac{105}{7}-\frac{105}{5}=-15+(-21)=-36$$

This does not give us the right answer, but we made an error in our calculation. We forgot to simplify the two fractions before subtracting them. Let's redo the calculation:

$$\frac{105}{7}-\frac{105}{5}=\frac{15\cdot7}{7}-\frac{21\cdot5}{5}=15-21=-6$$

This confirms that x=105 is indeed the correct solution. Therefore, the answer is B)105.

Solve the Equation and Check the Solution x7−x5=−6\frac { x } { 7 } - \frac { x } { 5 } = - 67x​−5x​=−6

Solve the Equation and Check the Solution $\frac { x } { 7 } - \frac { x } { 5 } = - 6$