55/18=17/16+1/2x
To solve this equation, we need to isolate the variable on one side of the equation. Let's begin by simplifying both sides of the equation.
First, let's simplify the right side of the equation: 17/16 + (1/2)x
We can find the common denominator for the fractions, which is 16.
17/16 + (1/2)x = (17/16) + (8/16)x
Now, let's simplify the left side of the equation: 55/18
To add or subtract fractions, they need to have the same denominator. To convert 55/18 into a fraction with a denominator of 16, we can multiply the numerator (55) and the denominator (18) by 8.
(55*8)/(18*8) = 440/144 = 55/18
Now our equation becomes:
55/18 = (17/16) + (8/16)x
To combine the fractions on the right side of the equation:
55/18 = (17 + 8x) / 16
To get rid of the fraction, we can cross-multiply:
55 * 16 = 18 * (17 + 8x)
Now, let's simplify the equation further:
880 = 306 + 144x
Next, we can isolate the variable by moving the constant term to the other side of the equation:
880 - 306 = 144x
574 = 144x
Finally, we can solve for x by dividing both sides of the equation by 144:
574/144 = x
x = 3.9861 (rounded to four decimal places)
Therefore, the value of x that satisfies the equation 55/18 = 17/16 + (1/2)x is approximately 3.9861.