x+1/6=-2/3
solution set?
LCD=6 so you multiply all number by 6.
denominators cancel out
6x + 6 = -4
6x = -10
x = -6/10 or -3/5
X + 1/6 = -2/3.
Multiply both sides by 6 and get:
6x + 1 = -4,
6x = -1 -4 = -5,
x = -5/6.
To solve the given equation x + 1/6 = -2/3, we can follow these step-by-step instructions:
Step 1: Isolate the variable term.
To get rid of the 1/6 on the left side, we need to subtract 1/6 from both sides of the equation:
x + 1/6 - 1/6 = -2/3 - 1/6
This simplifies to:
x = -2/3 - 1/6
Step 2: Find a common denominator for the fractions.
To add or subtract fractions, we need to have the same denominator. The least common denominator (LCD) for 3 and 6 is 6.
Step 3: Convert the fractions to have the same denominator.
In this case, -2/3 is already over 3 as the denominator, so we just need to convert 1/6 to have a denominator of 6:
1/6 = (1/6) * (2/2) = 2/12
Step 4: Perform the subtraction.
Now that both fractions have the same denominator, we can subtract them:
x = -2/3 - 2/12
Step 5: Simplify the result.
To subtract fractions, we subtract the numerators and keep the denominator the same:
x = (-2)/3 - 2/12
Common denominator: 12
x = (-8)/12 - 2/12
x = (-10)/12
Step 6: Reduce the fraction to simplest form (if necessary).
The fraction (-10)/12 can be reduced by dividing both the numerator and denominator by their greatest common divisor (GCD) of 2:
x = (-10)/12 = (-5)/6
So, the solution to the equation x + 1/6 = -2/3 is x = -5/6.