a-2/6 -5 = a+3/3
SOLVE FOR A
solving equations with fractions
To solve the equation for "a," you'll need to follow these steps:
Step 1: Simplify both sides of the equation.
Let's simplify the left side of the equation:
a - (2/6) - 5
Note that -(2/6) is the same as -1/3, as both -2 and 6 can be divided by 2. Therefore, the equation becomes:
a - 1/3 - 5
Simplify the right side of the equation:
a + (3/3)
Since both 3 and 3 have the same denominator, we can add them and get:
a + 1
So, the equation becomes:
a - 1/3 - 5 = a + 1
Step 2: Get rid of the fractions.
To eliminate the fractions, we need to find a common denominator for all the fractions involved. The least common multiple (LCM) of the denominators is 3.
So, let's multiply the entire equation by 3 to cancel out the denominators. Multiplying by 3 gives us:
3(a - 1/3 - 5) = 3(a + 1)
Expanding the equation, we have:
3a - 1 - 15 = 3a + 3
Step 3: Simplify the equation further.
Combine like terms on both sides:
3a - 16 = 3a + 3
Here, you can observe that the term "3a" is the same on both sides of the equation, which means it will cancel out.
Step 4: Solve for "a."
After canceling out the "3a" terms, we are left with:
-16 = 3
However, we can see that -16 and 3 are not equal, which means the equation has no solution. Therefore, the equation is inconsistent, and there is no value of "a" that satisfies it.
Hence, the equation has no solution for "a."
I have a feeling you meant:
(a-2)/6 - 5 = (a+3)/3
multiply each term by 6
a-2 + 30 = 2a + 6
-a = 6+2-30
a = 22
the way you typed it, the equation would simplify to
a - 1/3 - 5 = a + 1
the a's would drop out, and there would be no solution.