Solve.
5/8x + 1/16x=3/16 + x
To solve the equation 5/8x + 1/16x = 3/16 + x, we can start by combining like terms on both sides of the equation.
First, let's find a common denominator for the fractions on the left side. The least common multiple of 8 and 16 is 16. So let's rewrite the equation with this common denominator:
(10/16)x + (1/16)x = 3/16 + x
Now, we can combine the fractions on the left side by adding their numerators:
(10/16 + 1/16)x = 3/16 + x
This simplifies to:
(11/16)x = 3/16 + x
To get rid of the fraction on the right side, we can multiply both sides of the equation by 16:
16 * (11/16)x = 16 * (3/16 + x)
This gives us:
11x = 3 + 16x
Now, let's isolate the variable x by moving all terms with x to one side of the equation:
11x - 16x = 3
Combine like terms:
-5x = 3
Finally, divide both sides of the equation by -5 to solve for x:
x = 3/(-5)
Thus, the solution to the equation 5/8x + 1/16x = 3/16 + x is x = -3/5.
Convert the x terms to fractions with a common denominator and add them up
(11/16) x = 3/16 + x
Subtract x from both sides of the equation.
(-5/16)x = 3/16
Now multiply both sides by -16/5 for the answer