Solving the Equation: 1/2 + 7/9 = x + 4/5x
In this article, we will solve the equation 1/2 + 7/9 = x + 4/5x. This equation involves fractions, which can make it a bit more challenging to solve. But don't worry, we'll break it down step by step.
Step 1: Simplify the Equation
First, let's simplify the equation by combining the fractions on the left-hand side:
(1/2) + (7/9) = x + (4/5)x
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 2 and 9 is 18. So, we can convert both fractions to have a denominator of 18:
(9/18) + (14/18) = x + (4/5)x
Now, we can add the fractions:
(23/18) = x + (4/5)x
Step 2: Isolate x
Our goal is to isolate x on one side of the equation. To do this, we can subtract (4/5)x from both sides:
(23/18) - (4/5)x = x - (4/5)x
This simplifies to:
(23/18) = (1 - 4/5)x
Step 3: Solve for x
Now, we can solve for x by dividing both sides by (1 - 4/5):
x = (23/18) / (1 - 4/5)
To simplify this expression, we can convert the fraction (1 - 4/5) to a decimal:
x = (23/18) / (0.2)
x ≈ 1.28
Therefore, the value of x is approximately 1.28.
And that's it! We have successfully solved the equation 1/2 + 7/9 = x + 4/5x.
