Which expression is equivalent to one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x?
one and three fifths times x plus four
four fifteenths times x minus 4
negative four fifteenths times x minus four
negative 4 over fifteen times x plus four
The expression that is equivalent to one third times the quantity 2 times x plus 12 minus 14 over 15 times x is:
Negative 4 over fifteen times x plus four.
To find the equivalent expression, follow these steps:
1. Start with the original expression: 1/3 * (2x + 12) - (14/15) * x.
2. Simplify the first term by distributing 1/3 to the terms inside the parentheses: (1/3)*2x + (1/3)*12 - (14/15)*x.
3. Simplify each term within the expression: (2/3)x + 4 - (14/15)x.
4. Combine like terms by subtracting (14/15)x from (2/3)x: (2/3 - 14/15)x + 4.
5. Find a common denominator of 3 and 15, which is 15: [(2*5 - 14*3)/(3*5)]x + 4.
6. Simplify the numerator by multiplying: (-8/15)x + 4.
7. Rearrange the terms in descending order: 4 - (8/15)x.
Therefore, the expression equivalent to the original expression is: negative 8 over 15 times x plus 4, which can also be written as -8/15x + 4.
To find the equivalent expression, we need to simplify the given expression step by step.
The original expression is:
1/3 * (2x + 12) - (14/15) * x
First, distribute 1/3 to (2x + 12):
(1/3 * 2x) + (1/3 * 12) - (14/15) * x
This simplifies to:
(2/3 * x) + (4/3) - (14/15) * x
Next, find a common denominator for 3 and 15, which is 15. Multiply the fractions to match the common denominator:
(2/3 * x) + (4/3) - (14/15 * x) = (10/15 * x) + (20/15) - (14/15 * x)
Now, combine like terms by adding or subtracting coefficients of x and the constant terms:
(10/15 * x - 14/15 * x) + (20/15) = (-4/15 * x) + (20/15)
The equivalent expression is:
-4/15 * x + 20/15
To simplify further, we can divide both the numerator and denominator by their greatest common divisor, which is 5. This gives us:
(-4/15 * x) + (20/15) = -4/15 * x + 4/3
So, the correct answer is negative 4 over fifteen times x plus four