[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
- [tex] \tt- \frac{ 1 }{ 2 } d+ \frac{ 3 }{ 8 } -d = \frac{ 1 }{ 4 } + \frac{ 3 }{ 4 } d+2 \\ [/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt- \frac{ 1 }{ 2 } d+ \frac{ 3 }{ 8 } -d = \frac{ 1 }{ 4 } + \frac{ 3 }{ 4 } d+2 \\ [/tex]
Combine [tex]\tt-\frac{1}{2}d[/tex] and -d to get [tex]\tt-\frac{3}{2}d[/tex].
[tex] \tt-\frac{3}{2}d+\frac{3}{8}=\frac{1}{4}+\frac{3}{4}d+2 \\ [/tex]
Because 1/4 and 8/4 have the same denominator, add them by adding their numerators.
[tex] \tt-\frac{3}{2}d+\frac{3}{8}=\frac{1+8}{4}+\frac{3}{4}d \\ [/tex]
Subtract [tex]\tt\frac{3}{4}d[/tex] from both sides.
[tex] \tt-\frac{3}{2}d+\frac{3}{8}-\frac{3}{4}d=\frac{9}{4} \\ [/tex]
Combine [tex]\tt-\frac{3}{2}d[/tex] and [tex]\tt-\frac{3}{4}d[/tex] to get [tex]\tt-\frac{9}{4}d[/tex].
[tex] \tt-\frac{9}{4}d+\frac{3}{8}=\frac{9}{4} \\ [/tex]
Subtract 3/8 from both sides.
[tex] \tt-\frac{9}{4}d=\frac{9}{4}-\frac{3}{8} \\ [/tex]
The least common multiple of 4 and 8 is 8. Convert 9/4 and 3/8 to fractions with denominator 8.
[tex] \tt-\frac{9}{4}d=\frac{18}{8}-\frac{3}{8} \\ [/tex]
Because 18/8 and 3/8 have the same denominator, subtract them by subtracting their numerators.
[tex] \tt-\frac{9}{4}d=\frac{18-3}{8} \\ [/tex]
Subtract 3 from 18 to get 15.
[tex] \tt-\frac{9}{4}d=\frac{15}{8} \\ [/tex]
Multiply both sides by - 4/9, the reciprocal of -9/4.
[tex] \tt \: d=\frac{15}{8}\left(-\frac{4}{9}\right) \\ [/tex]
Multiply 15/8 by -4/9 by multiplying the numerator by the numerator and the denominator by the denominator.
[tex] \tt \: d=\frac{15\left(-4\right)}{8\times 9} \\ [/tex]
Carry out the multiplications in the fraction ⇨ [tex]\tt\frac{15\left(-4\right)}{8\times 9}[/tex].
[tex] \tt \: d=\frac{-60}{72} \\ [/tex]
Reduce the fraction -60/72 to its lowest terms by extracting and cancelling out 12.
[tex] \boxed{ \boxed{ \bf \: d=-\frac{5}{6}\approx -0.833..}}[/tex]
