Solve the equation. Choose the method you prefer to use. Check your answer.
b/13 - 9b/13 = 48/13
To solve the equation b/13 - 9b/13 = 48/13, we can combine the like terms on the left side of the equation.
b/13 - 9b/13 can be simplified to (1 - 9b)/13.
So now, our equation becomes (1 - 9b)/13 = 48/13.
To isolate the variable, we can multiply both sides of the equation by 13:
13 * (1 - 9b)/13 = 13 * (48/13).
This simplifies to (1 - 9b) = 48.
Next, let's isolate the variable term by subtracting 1 from both sides of the equation:
(1 - 9b) - 1 = 48 - 1.
This simplifies to 1 - 9b - 1 = 47.
Simplifying further, we have -9b = 47.
To solve for b, we can divide both sides of the equation by -9:
-9b/-9 = 47/-9.
This simplifies to b = -47/9.
So the solution to the equation is b = -47/9.
To check our answer, we can substitute b = -47/9 back into the original equation:
(-47/9)/13 - 9(-47/9)/13 = 48/13.
(-47/9)*(1/13) - 9*(-47/9)*(1/13) = 48/13.
-47/117 - 9*(-47/117) = 48/13.
-47/117 + 423/117 = 48/13.
(-47 + 423)/117 = 48/13.
376/117 = 48/13.
We can see that both sides of the equation are equal, so our solution b = -47/9 is correct.
To solve the equation (b/13) - (9b/13) = 48/13, we can combine the two fractions with common denominators:
(b - 9b) / 13 = 48/13
To simplify the equation, combine the like terms on the left side:
(-8b) / 13 = 48/13
Now, multiply both sides of the equation by the reciprocal of the left side coefficient to isolate the variable:
[(13/8) * (-8b)] / 13 = (48/13) * (13/8)
Simplifying further, we have:
b = 48/8
b = 6
To check the solution, substitute b = 6 back into the original equation:
(6/13) - (9(6)/13) = 48/13
(6/13) - (54/13) = 48/13
Multiplying both fractions by their least common denominator, 13:
6 - 54 = 48
-48 = 48
Since -48 is not equal to 48, the solution b = 6 is incorrect. There may have been an error in the calculations. Let's try solving the equation again.
To solve the equation b/13 - 9b/13 = 48/13, we can use the method of combining like terms and isolating the variable.
Step 1: Combine Like Terms
We have two terms with b/13, so we can combine them by subtracting the coefficients:
b/13 - 9b/13 = (1 - 9)b/13 = -8b/13
Step 2: Isolate the Variable
Now that we have -8b/13 on one side of the equation, we can isolate the variable by multiplying both sides of the equation by 13:
13 * (-8b/13) = 13 * (48/13)
On the left side, the 13 cancels out with the 13 in the denominator, and on the right side, the 13 cancels out with the 13 in the numerator:
-8b = 48
Step 3: Solve for b
To solve for b, divide both sides of the equation by -8:
(-8b)/(-8) = 48/(-8)
On the left side, the -8 cancels out, and on the right side, divide 48 by -8:
b = -6
Step 4: Check the Answer
To check the solution, substitute b = -6 back into the original equation:
(-6)/13 - 9(-6)/13 = 48/13
Simplifying both sides of the equation:
-6/13 + 54/13 = 48/13
48/13 = 48/13
Since both sides of the equation are equal, the solution b = -6 is correct.
So, the solution to the equation b/13 - 9b/13 = 48/13 is b = -6.