Question

Please help me I’ll give 50 points. Tysm

Answer 1

`\textsf{A)} \quad -1(3)/(20)y+4`

Explanation:

Given expression:

`\left(11-9 (3)/(5)y\right)+\left(8 (9)/(20)y-7 \right)`

Remove the parentheses:

`11-9 (3)/(5)y+8 (9)/(20)y-7`

Collect like terms:

`8 (9)/(20)y-9 (3)/(5)y+11-7`

Subtract the numbers 11 - 7:

`8 (9)/(20)y-9 (3)/(5)y+4`

Factor out y:

`\left(8 (9)/(20)-9 (3)/(5)\right)y+4`

Partition the mixed numbers into fractions and whole numbers, and then subtract them separately.

Subtract the whole numbers:

`\implies 8-9=-1`

Subtract the fractions by changing both fractions into equivalent fractions so both fractions have the same denominator:

`\implies (9)/(20)-(3)/(5)`

`\implies (9)/(20)-(3 \cdot 4)/(5 \cdot 4)`

`\implies (9)/(20)-(12)/(20)`

`\implies -(3)/(20)`

Put the two answers from the whole numbers and fractions back together:

`\implies -1-(3)/(20)=- \left(1+(3)/(20)\right)=-1(3)/(20)`

Therefore:

`\left(8 (9)/(20)-9 (3)/(5)\right)y+4=\left(-1(3)/(20)\right)y+4=-1(3)/(20)y+4`