How would i solve this x+7/14=1-3/7x
(x+7)/14 = 1 - 3/7 x
x/14 + 7/14 = 1 - 3/7 x
x/14 + 3/7 x = 1 - 1/2
x/2 = 1/2
x = 1
To solve the equation x + 7/14 = 1 - 3/7x, you need to isolate the variable x on one side of the equation. Here's a step-by-step explanation of how to solve it:
Step 1: Distribute -3/7 to x on the right side of the equation:
x + 7/14 = 1 - (3/7)x
Step 2: Simplify the equation by combining like terms:
x + 7/14 = 1 - 3x/7
Step 3: Convert the fractions to a common denominator:
x + 7/14 = 14/14 - 6x/14
Step 4: Combine the fractions on the right side:
x + 7/14 = (14 - 6x)/14
Step 5: Multiply both sides of the equation by 14 to eliminate the denominators:
14(x + 7/14) = 14((14 - 6x)/14)
Simplifying further:
x + 7 = 14 - 6x
Step 6: Combine like terms by subtracting x from both sides:
x + 7 - x = 14 - 6x - x
Simplifying further:
7 = 14 - 7x
Step 7: Isolate the variable term by subtracting 14 from both sides:
7 - 14 = 14 - 7x - 14
Simplifying further:
-7 = -7x
Step 8: Divide both sides of the equation by -7 to solve for x:
-7 / -7 = -7x / -7
Simplifying further:
1 = x
So, the solution to the equation x + 7/14 = 1 - 3/7x is x = 1.