Solve the equation. Choose the method you prefer to use. Check your answer.
b/13 - 9b/13 = 48/13
b=
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 = (b - 9b)/13 = -8b/13
So the equation becomes -8b/13 = 48/13.
To isolate the variable b, we can multiply both sides of the equation by 13:
13 * (-8b/13) = 13 * (48/13)
-8b = 48
Dividing both sides of the equation by -8 gives us:
b = 48/(-8)
b = -6
To check our answer, we substitute b = -6 back into the original equation:
-6/13 - (9 * -6)/13 = 48/13
Simplifying the left side, we get:
-6/13 + 54/13 = 48/13
Combining the like terms, we have:
48/13 = 48/13
Since the equation is true, our answer b = -6 is correct.
To solve the equation b/13 - 9b/13 = 48/13, we can use the method of combining like terms.
First, let's combine the terms on the left side of the equation:
b/13 - 9b/13 = (b - 9b)/13
Simplifying further, we have:
(b - 9b)/13 = -8b/13
Now, we can rewrite the equation as:
-8b/13 = 48/13
To isolate the variable b, we can multiply both sides of the equation by 13:
13 * (-8b/13) = 13 * (48/13)
This simplifies to:
-8b = 48
Finally, we solve for b by dividing both sides of the equation by -8:
b = 48 / -8
Dividing, we find:
b = -6
To verify if this answer is correct, let's substitute the value of b back into the original equation:
(-6/13) - 9(-6/13) = 48/13
Calculating:
-6/13 + 54/13 = 48/13
Combining the terms on the left side, we get:
48/13 = 48/13
Since both sides of the equation are equal, our solution of b = -6 is correct.
To solve the equation b/13 - 9b/13 = 48/13, we can begin by combining the two fractions on the left side of the equation:
b/13 - 9b/13 = (b - 9b) /13 = -8b/13
The equation now becomes -8b/13 = 48/13.
To isolate the variable b, we can multiply both sides of the equation by the reciprocal of -8/13, which is -13/8. This will result in:
(-13/8) * (-8b/13) = (-13/8) * (48/13)
After simplifying, we have:
b = -624/104
Further simplification can be done by dividing both the numerator and denominator by their greatest common divisor (GCD) since -624 and 104 are both divisible by 8:
b = -624/104 = -6/1
Therefore, the solution to the equation b/13 - 9b/13 = 48/13 is b = -6.
To check our answer, we can substitute b = -6 back into the original equation:
(-6)/13 - 9(-6)/13 = 48/13.
After simplification, we have:
-6/13 + 54/13 = 48/13
Now, adding the fractions on the left side of the equation:
(-6 + 54) / 13 = 48/13
48/13 = 48/13
Since both sides of the equation are equal, our solution of b = -6 is correct.