Complete the following stepped-out solution to show that is equivalent to .

Question

(1 point)
15 + g + ⋅
3
2
2
3
16 + g
15 + g + ⋅
3
2
2
3
15 + g+
15+ +g
16 + G

Answer 1

To prove that  is equivalent to , we need to show that they have the same value when simplified.

Given expression: 15 + g + ⋅
───────────────────
3
2
2
3

Step 1: Simplify the numerator. In the numerator, we have 15 + g + 2/3.

Step 2: Simplify the denominator. In the denominator, we have 2/3.

Step 3: Divide the numerator by the denominator. We can rewrite the division as a multiplication by the reciprocal. So, we have:

(15 + g + 2/3) × (3/2)

Step 4: Distribute the multiplication. Multiplying each term in the numerator by 3/2, we get:

(15 × 3/2) + (g × 3/2) + (2/3 × 3/2)

Step 5: Simplify the terms in the numerator. Multiplying and adding, we get:

(45/2) + (3g/2) + (6/6)

Step 6: Simplify the fraction. Adding the fractions, we get:

(45/2) + (3g/2) + 1

Step 7: Combine like terms. We have:

(45 + 3g + 2)/2 + 1

Step 8: Simplify the numerator further. Adding the terms, we get:

(47 + 3g)/2 + 1

So, we can conclude that  is equivalent to (47 + 3g)/2 + 1.