(x+3)/8-(x-3)/10=(x-5)/4-11/8

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Jun 09, 2024

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Solving the Equation: (x+3)/8 - (x-3)/10 = (x-5)/4 - 11/8

In this article, we will solve the equation (x+3)/8 - (x-3)/10 = (x-5)/4 - 11/8. This equation involves fractions and variables, and we will use algebraic manipulation to find the value of x.

Step 1: Simplify the Equation

First, let's simplify the equation by combining the fractions on each side:

(x+3)/8 - (x-3)/10 = (x-5)/4 - 11/8

Step 2: Get a Common Denominator

To combine the fractions, we need to get a common denominator. The least common multiple (LCM) of 8, 10, and 4 is 40. So, we will convert each fraction to have a denominator of 40:

(5x+15)/40 - (4x-12)/40 = (10x-50)/40 - (44)/40

Step 3: Combine Like Terms

Now, let's combine like terms:

(5x+15)/40 - (4x-12)/40 = (10x-50)/40 - (44)/40

Combine the numerators:

(5x - 4x + 15 + 12)/40 = (10x - 50 - 44)/40

Simplify:

(x + 27)/40 = (10x - 94)/40

Step 4: Cross-Multiply

Now, let's cross-multiply to eliminate the fractions:

40(x + 27) = 40(10x - 94)

Step 5: Simplify and Solve

Expand and simplify the equation:

40x + 1080 = 400x - 3760

Subtract 40x from both sides:

1080 = 360x - 3760

Add 3760 to both sides:

4840 = 360x

Divide both sides by 360:

x = 4840/360

x = 13.44

Therefore, the value of x is approximately 13.44.

Conclusion

In this article, we have successfully solved the equation (x+3)/8 - (x-3)/10 = (x-5)/4 - 11/8 and found the value of x to be approximately 13.44.