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.