Solve the equation below. Choose the method you prefer to use. Check your answer.
n/8 - 7n/16 =1/8
n=
To solve the equation, we can start by getting rid of the fractions. One way to do this is by multiplying every term in the equation by the least common denominator (LCD), which is 16 in this case.
Multiplying n/8 by 16 gives us (16/8)n = 2n.
Multiplying 7n/16 by 16 gives us 7n.
Multiplying 1/8 by 16 gives us 2.
So, the equation becomes 2n - 7n = 2.
Combining like terms, we have:
-5n = 2.
Dividing both sides of the equation by -5 gives us:
n = -2/5.
To check the answer, substitute n = -2/5 back into the original equation:
(-2/5)/8 - 7(-2/5)/16 = 1/8.
This simplifies to:
(-2/40) - (-14/40) = 1/8,
-2/40 + 14/40 = 1/8,
12/40 = 1/8,
3/10 = 1/8.
Since this is not a true statement, the answer n = -2/5 is incorrect.
To solve the equation n/8 - 7n/16 = 1/8, we can follow these steps:
Step 1: Multiply every term in the equation by the common denominator, which is 16.
16(n/8) - 16(7n/16) = 16(1/8)
This simplifies to:
2n - 7n = 2
Step 2: Combine like terms on the left side of the equation.
-5n = 2
Step 3: Divide both sides of the equation by -5 to isolate the variable n.
-5n / -5 = 2 / -5
This simplifies to:
n = -2/5
To check our answer, we can substitute n = -2/5 back into the original equation and see if both sides are equal.
(-2/5)/(8) - 7(-2/5)/(16) = 1/8
This simplifies to:
-1/20 + 7/40 = 1/8
-2/40 + 7/40 = 1/8
5/40 = 1/8
1/8 = 1/8
Since both sides of the equation are equal, we can conclude that the solution n = -2/5 is correct.
To solve the equation n/8 - 7n/16 = 1/8, we can follow these steps:
Step 1: Get rid of the fractions by multiplying every term in the equation by the least common denominator (LCD), which is 16. This will eliminate the denominators.
16 * (n/8) - 16 * (7n/16) = 16 * (1/8)
After simplifying, we get:
2n - 7n = 2
Step 2: Combine like terms. In this case, we combine the n terms on the left side.
-5n = 2
Step 3: Solve for n by dividing both sides of the equation by -5.
n = 2 / -5
Simplifying further, we have:
n = -2/5
To check our answer, substitute -2/5 back into the original equation and see if both sides are equal.
LHS: (-2/5)/8 - 7(-2/5)/16
= -2/40 + 14/40
= 12/40
= 3/10
RHS: 1/8
Since the LHS is equal to the RHS, our answer is correct.
Therefore, the solution to the equation n/8 - 7n/16 = 1/8 is n = -2/5.