1/2(x+8)=1/3(x-9)

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Jun 16, 2024

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Solving the Equation: 1/2(x+8) = 1/3(x-9)

In this article, we will solve the equation 1/2(x+8) = 1/3(x-9) step by step.

Step 1: Multiply both sides by the Least Common Multiple (LCM)

The LCM of 2 and 3 is 6. Therefore, we multiply both sides of the equation by 6 to eliminate the fractions.

6 × [1/2(x+8)] = 6 × [1/3(x-9)]
3(x+8) = 2(x-9)

Step 2: Simplify both sides of the equation

Now, we simplify both sides of the equation:

3x + 24 = 2x - 18

Step 3: Isolate the variable x

To isolate x, we add 18 to both sides of the equation and subtract 2x from both sides:

3x + 24 = 2x - 18
3x - 2x = -18 - 24
x = -42/1
x = -42

Therefore, the value of x is -42.

Conclusion

In this article, we solved the equation 1/2(x+8) = 1/3(x-9) using the steps mentioned above. The value of x is -42.