Answer:
1) Which expression is equal to
[tex] \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:
[tex] \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} [/tex]
[tex] \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)[/tex]
[tex] \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) [/tex]
[tex] \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)[/tex]
[tex] \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} [/tex]
[tex] \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}[/tex]
4) Which expression is equal to
[tex] \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)[/tex]
[tex] \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}[/tex]
5) Which expression is equal to
[tex] \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
Step-by-step explanation:
[tex] \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x[/tex]
[tex] \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2[/tex]
[tex] \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}[/tex]
