Determine which expression is equivalent to the expression 2 over 3 times g minus 5 minus 11 over 15 times g minus the expression one over 5 times g plus 12.
4 over 15 times g plus negative 17
negative 4 over 15 times g plus negative 17
2 over 15 times g plus negative 7
negative 4 over 15 times g plus negative 7
To solve this problem, first simplify each expression separately. The first expression, 2/3 times g minus 5, can be simplified as (2/3)g - 5. The second expression, 11/15 times g plus 12, can be simplified as (11/15)g + 12.
Now, subtract the second expression from the first expression, by distributing the negative sign:
(2/3)g - 5 - ((11/15)g + 12)
= (2/3)g - 5 - (11/15)g - 12
= (2/3 - 11/15)g - 5 - 12
Now, find a common denominator to combine the fractions:
(10/15 - 11/15)g - 17
= (-1/15)g - 17
The equivalent expression to the original expression is therefore -1/15 times g minus 17.
Answer: negative 1/15 times g plus negative 17.
To determine which expression is equivalent to the given expression, we need to simplify it step by step.
The given expression is:
2/3 * g - 5 - 11/15 * g - (1/5 * g + 12)
First, let's simplify the subtraction inside the brackets:
2/3 * g - 5 - 11/15 * g - 1/5 * g - 12
To combine the terms with "g," we need to have a common denominator for 3, 15, and 5, which is 15. We can convert the fractions to have a common denominator:
(10/15 * g) - 5 - (11/15 * g) - (3/15 * g + 12)
Combine like terms:
(-1/15 * g) - 5 - 12
Simplify further:
-1/15 * g - 17
So, the expression is equivalent to:
-1/15 * g - 17
Therefore, the correct answer is: negative 1/15 times g plus negative 17.
To determine which expression is equivalent to the given expression, let's simplify it step by step:
Expression: 2/3 * g - 5 - 11/15 * g - (1/5 * g + 12)
Step 1: Simplify the terms with "g":
2/3 * g - 11/15 * g - 1/5 * g = (2/3 - 11/15 - 1/5) * g
Step 2: Find a common denominator for the fractions:
The common denominator for 3, 15, and 5 is 15.
Step 3: Convert the fractions to have a denominator of 15:
(2/3 * (5/5) - 11/15 * (1/1) - 1/5 * (3/3)) * g = (10/15 - 11/15 - 3/15) * g
Step 4: Combine the fractions:
(10 - 11 - 3) / 15 * g = (-4/15) * g
Step 5: Simplify the expression:
-4/15 * g - 5 - 12 = (-4/15) * g - 17
Therefore, the expression equivalent to the given expression is: negative 4 over 15 times g plus negative 17.