Solve. Please show step by step process.
5/8 x+1/16 x=11/16+x
multiply both sides by 16
collect x terms on one side.
5/8 x+1/16 x=11/16+x
16*(5/8 x+1/16 x) = 16(11/16+x)
80 + x + 16 + x= 11 + 16x
80 + 2x + 16 = 11 + 16x
-x = 18x (divide by 1)
x = 18
Did I do this correctly?
To solve the equation (5/8)x + (1/16)x = (11/16) + x, we will combine like terms and isolate the variable x. Here are the step-by-step process:
Step 1: Find a common denominator.
The common denominator for 8 and 16 is 16. So, we can rewrite the equation as:
(10/16)x + (1/16)x = (11/16) + x
Step 2: Combine like terms on the left side of the equation.
(10/16)x + (1/16)x simplifies to (11/16)x. So, the equation becomes:
(11/16)x = (11/16) + x
Step 3: Bring all the terms involving x to one side of the equation.
To do this, we subtract x from both sides of the equation:
(11/16)x - x = (11/16)
On the left side of the equation, we can combine the fractions:
[(11/16) - (16/16)]x = (11/16)x - x = (11/16 - 16/16)x = -5/16 x
So, the equation is now:
(-5/16)x = (11/16)
Step 4: Solve for x.
To solve for x, we need to multiply both sides of the equation by the reciprocal of -5/16, which is -16/5:
x = (11/16) * (-16/5)
We can simplify this expression by canceling out common factors:
x = (11 * -16) / (16 * 5)
x = -176 / 80
x = -2.2
Therefore, the solution to the equation is x = -2.2.