5/8x + 1/16x = 7/16 + x
The solution is x=
Multiply both sides by 16.
10x + x = 7 + 16x
Subtract 16x from both sides.
11x - 16 x = 7
-5x = 7
x = -5/7
5(x+7)=10x+12=
To solve this equation, we can start by simplifying both sides:
On the left side, we can find a common denominator for the fractions. Since 8 and 16 have a common multiple of 16, we can rewrite the equation as:
(5/8)x + (1/16)x = (7/16) + x
To add the fractions, we need a common denominator. We can convert 5/8 to 10/16 (∵ 10/16 = 5/8 * 2/2) and leave 1/16 as it is. So the equation becomes:
(10/16)x + (1/16)x = (7/16) + x
Now we can combine the fractions on the left side by adding the numerators while keeping the denominator the same:
(11/16)x = (7/16) + x
Next, we can isolate the variable x by subtracting x from both sides of the equation:
(11/16)x - x = (7/16)
This simplifies to:
(11/16 - 16/16)x = (7/16)
Now, combine like terms on the left side:
(-5/16)x = (7/16)
To find x, we need to get rid of the fraction coefficient (-5/16) on x. To do this, we can multiply both sides of the equation by the reciprocal of (-5/16), which is (-16/5):
((-16/5) * (-5/16))x = ((-16/5) * (7/16))
This simplifies to:
x = (-16/5)*(7/16)
Now we can multiply the numerators and the denominators:
x = -112/80
The fraction -112/80 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8:
x = (-112/8) / (80/8)
This simplifies to:
x = -14/10
Finally, we can simplify the fraction by dividing both the numerator and the denominator by 2:
x = (-14/2) / (10/2)
x = -7/5
Therefore, the solution to the equation is x = -7/5.