Question

(25 points) Please help me I'm stuck on these 3 questions.

Answer 1

1) Which expression is equal to

`\bf\bigg( - 3 (1)/(4) d + (3)/(5) \bigg) - \bigg(2 (7)/(8) d + (7)/(10) \bigg)`

`\bf \longrightarrow \boxed{ - (49)/(8)d - (1)/(10) } \: {\underline{\underline{ans}}}`

Explanation:

`\bf \longrightarrow \bigg( - 3 (1)/(4) d + (3)/(5) \bigg) - \bigg(2 (7)/(8) d + (7)/(10) \bigg)`

`\bf \longrightarrow \bigg( - (4 * 3 + 1)/(4) d + (3)/(5) \bigg ) - \bigg((8 * 2 + 7)/(8) d + (7)/(10) \bigg)`

`\bf \longrightarrow\bigg( ( - 13)/(4)d + (3)/(5) \bigg) - \bigg( (23)/(8)d + (7)/(10) \bigg)`

`\bf \longrightarrow ( - 13)/(4)d + (3)/(5) + ( - 23)/(8) d + ( - 7)/(10)`

`\bf \longrightarrow \bigg( ( - 13)/(4)d + ( - 23)/(8)d \bigg) + \bigg( (3)/(5) + ( - 7)/(10) \bigg)`

`\bf \longrightarrow \bigg( ((2 * - 13) + (1 * - 23) )/(8)d \bigg) + \bigg( ((2 * 3) + (1 * - 7))/(10) \bigg)`

`\bf \longrightarrow \bigg( ( (- 26) + ( - 23))/(8)d \bigg) + \bigg( ((6) + ( - 7))/(10) \bigg)`

`\bf \longrightarrow\bigg( ( - 26 - 23)/(8) d\bigg) + \bigg( (6 - 7)/(10) \bigg)`

`\bf \longrightarrow( - 49)/(8)d + ( - 1)/(10)`

`\bf \longrightarrow \boxed{ - (49)/(8)d - (1)/(10) } \: {\underline{\underline{ans}}}`

4) Which expression is equal to

`\bf\bigg( - 2 (1)/(2) n + (1)/(4) \bigg) + \bigg(3 (3)/(4) n - (5)/(8) \bigg)`

`\bf \longrightarrow \boxed{(5)/(4)n - (3)/(8) } \: {\underline{\underline{ans}}}`

5) Which expression is equal to

`\bf(1)/(5)(3x + 10) - (11)/(15)x`

`\bf \longrightarrow \boxed{(-2)/(15)x + 2} \: {\underline{\underline{ans}}}`

Explanation:

`\bf\longrightarrow(1)/(5)(3x + 10) - (11)/(15)x`

`\bf\longrightarrow(1)/(5)(3x) + (1)/(5)(10) + (-11)/(15)x`

`\bf\longrightarrow(3)/(5)x + 2 + (-11)/(15)x`

`\bf\longrightarrow\bigg((3)/(5)x + (-11)/(15)x\bigg) + 2`

`\bf \longrightarrow \boxed{(-2)/(15)x + 2} \: {\underline{\underline{ans}}}`