5/2x+1/4x=9/4+x
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Please check if the original question is meant to be:
(5/2)x+(1/4)x=9/4+x, or perhaps
5x/2 + x/4 = 9/4 + x
If that's the case, we proceed to isolate terms containing x on the left, and constants on the right to get
5x/2 + x/4 -x = 9/4
(5/2+1/4-1)x = 9/4
(5/4)x = 9/4
x = 9/4 * (4/5)
Can you take it from here?
This was written the first way. Do you still calculate the same way? Thanks for the help!
Yes, both ways I have written give the same result.
I was afraid that it was:
5/(2x)+1/(4x)=9/4+x
in which case it would involve solving a quadratic equation.
To solve this equation, we need to find the value of x that makes the equation true. Let's go through the steps to solve it:
Step 1: Find a common denominator
In this equation, the denominators are 2x, 4x, and 4. To find a common denominator, we can multiply all the denominators together. In this case, the common denominator will be 8x.
Step 2: Multiply each term by the common denominator
By multiplying each term by 8x, we will eliminate the fractions. This step will help us simplify the equation. So, let's do that:
8x * (5/2x) + 8x * (1/4x) = 8x * (9/4) + 8x * (1)
The equation becomes:
(40 + 2) = 9x + 8x
Simplifying further:
42 = 17x
Step 3: Isolate the variable
To solve for x, we need to isolate it on one side of the equation. In this case, we want to have x terms on one side and constant terms on the other side. Let's move the constant term (42) to the other side by subtracting it:
42 - 42 = 17x - 42
0 = 17x - 42
Now, let's move the 17x term to the other side by adding it:
17x - 17x - 42 = 17x - 17x
-42 = 0
Step 4: Solve for x
Since the equation -42 = 0 is not true, it means there is no value of x that makes the original equation 5/2x+1/4x=9/4+x true. Therefore, this equation has no solution.
In conclusion, the equation has no solution because no value of x satisfies it.