Question

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

Answer 1

The simplified form of the expression 2/3 times g minus 5 minus 11/15 times g minus one over 5 times g plus 12 is -4/15g + 7, which means the equivalent expression is negative 4 over 15 times g plus negative 7.

Step-by-step explanation:

To determine which expression is equivalent to 2/3 times g minus 5 minus 11/15 times g minus one over 5 times g plus 12, we need to simplify and combine like terms. Let's break it down step by step:

1. Multiply the term g by the coefficients 2/3 and -11/15, and by -1/5 respectively.
2. Combine the numerical terms -5 and +12.
3. Since the coefficients 2/3, -11/15, and -1/5 have a common denominator of 15, we will convert them to have this common denominator and then sum them up.

Step 1:

• (2/3)g = (2*5)/(3*5)g = (10/15)g
• (-11/15)g is already in the form we need.
• (-1/5)g = (-3/15)g

Step 2:

• -5 + 12 = 7

Step 3:

• (10/15)g - (11/15)g - (3/15)g = (10 - 11 - 3)/15 g = (-4/15)g
• But there is also the numerical part, which is +7.

Putting it all together:

(-4/15)g + 7 is the simplified form of the given expression.

Therefore, the equivalent expression is negative 4 over 15 times g plus negative 7.