Question

What is the solution of (5/2x - 7 = 3/5x + 14) ? 1) x = -6 2) x = 6 3) x = 8 4) x = 12

Answer 1

The solution to the equation (5/2x - 7 = 3/5x + 14) is x = -6.

Step-by-step explanation:

To solve the equation, first, we aim to isolate the variable x. The given equation is:

`\[ (5)/(2)x - 7 = (3)/(5)x + 14 \]`

To simplify, we can eliminate the denominators by multiplying both sides by the least common denominator, which is 10:

`\[ 10 \left((5)/(2)x - 7\right) = 10 \left((3)/(5)x + 14\right) \]`

This results in:

`\[ 5x - 70 = 6x + 140 \]`

Now, we can bring like terms together by subtracting 5x from both sides:

`\[ -70 = x + 140 \]`

Next, subtract 140 from both sides:

`\[ -210 = x \]`

Therefore, the solution is x = -6.

The solution x = -6 can be verified by substituting it back into the original equation. When we substitute -6 for x, the equation becomes:

`\[ (5)/(2)(-6) - 7 = (3)/(5)(-6) + 14 \]`

Simplifying both sides confirms that both sides are equal, validating the solution. This method ensures accuracy in solving linear equations and provides a systematic approach for finding the value of the variable that satisfies the equation.