Please solve:
a. 1/3 - 5/6 = 1/x
b. t+1/3 - t-1/2 = 1
a. First, turn the left side of the equation into a single fraction, by using a common denominator.
1/3 - 5/6 = (2-5)/6 = -3/6 = -1/2
That leaves you with
-1/2 = 1/x
-x = 2
x = ?
b. t + 1/3 -t -1/2 = 1
has no solution, because the t terms cancel out, leaving you with a false statement.
You probably meant to write
(t+1)/3 - (t-1)/2 = 1
That does have a solution. Again, form a common denominator
[2(t+1) - 3(t-1)]/6 = 1
(-t +5)/6 = 1
Multiply both sides by 6 and combine constant terms.
-t + 5 = 6
-t = 1
t = ?
12,4
a. To solve the equation 1/3 - 5/6 = 1/x, we need to find the value of x that satisfies the equation.
Step 1: Find a common denominator for 1/3 and 5/6.
The least common multiple of 3 and 6 is 6. So, we can rewrite 1/3 as 2/6.
Step 2: Combine the fractions on the left-hand side of the equation.
2/6 - 5/6 = -3/6 = -1/2.
Step 3: Set up the equation with the combined fraction.
-1/2 = 1/x.
Step 4: Solve for x.
To solve for x, we can cross multiply:
-1 * x = 2 * 1,
which simplifies to -x = 2.
Step 5: Divide both sides by -1 to isolate x.
Dividing both sides by -1, we get:
x = -2.
So, the solution to the equation 1/3 - 5/6 = 1/x is x = -2.
b. To solve the equation t + 1/3 - t - 1/2 = 1, we need to find the value of t that satisfies the equation.
Step 1: Combine like terms on the left-hand side of the equation.
The t terms cancel each other out:
(t - t) + 1/3 - 1/2 = 1.
0 + 1/3 - 1/2 = 1.
Step 2: Find a common denominator for 1/3 and 1/2.
The least common multiple of 3 and 2 is 6. So, we can rewrite 1/3 as 2/6 and 1/2 as 3/6.
Step 3: Combine the fractions on the left-hand side of the equation.
2/6 - 3/6 = -1/6.
Step 4: Set up the equation with the combined fraction.
-1/6 = 1.
Step 5: Since -1/6 does not equal 1, there is no solution to the equation t + 1/3 - t - 1/2 = 1.
Therefore, the equation t + 1/3 - t - 1/2 = 1 has no solution.