Question

Simplify the given expression.

1/6(3x+5y)+2/3(3/5x-6y)

Answer 1

can u draw or put the screenshot of the question?

Answer 2

You don't have to draw it, just use the equation option. Would probably be easier :P

Answer 3

\[\frac{ 1 }{ 6 }\left( 3x+5y \right)+\frac{ 2 }{ 3 }\left( \frac{ 3 }{ 5 }x-6y \right)\]

Answer 4

Distribute the 1/6 and 2/3 first.

Answer 5

Cancel common terms in the numerator and denominator of \(\frac{3 (x-6 y)×2}{3×5}\).
\(\frac{3 (x-6 y)×2}{3×5} = \frac{3}{3}×\frac{(x-6 y)×2}{5} = \frac{(x-6 y)×2}{5}\):
\(\frac{3 x+5 y}{6}+\frac{2 (x-6 y)}{5}\)
Put the fractions in \(\frac{3 x+5 y}{6}+\frac{(x-6 y)×2}{5}\) over a common denominator.
Put each term in \(\frac{3 x+5 y}{6}+\frac{(x-6 y)×2}{5}\) over the common denominator 30: \(\frac{3 x+5 y}{6}+\frac{(x-6 y)×2}{5} = \frac{5 (3 x+5 y)}{30}+\frac{12 (x-6 y)}{30}:\)
\(\frac{5 (3 x+5 y)}{30}+\frac{12 (x-6 y)}{30}\)
Combine \(\frac{5 (3 x+5 y)}{30}+\frac{12 (x-6 y)}{30}\) into a single fraction.
\(\frac{5 (3 x+5 y)}{30}+\frac{12 (x-6 y)}{30} = \frac{5 (3 x+5 y)+12 (x-6 y)}{30:}\)
\(\frac{5 (3 x+5 y)+12 (x-6 y)}{30}\)
Distribute 5 over \(3 x+5 y.\)
\(5 (3 x+5 y) = 15 x+25 y:\)
\(\frac{15 x+25 y+12 (x-6 y)}{30}\)
Distribute 12 over \(x-6 y.\)
\(12 (x-6 y) = 12 x-72 y:\)
\(\frac{15 x+25 y+12 x-72 y}{30}\)
Group like terms in \(15 x+25 y+12 x-72 y.\)
Grouping like terms, \(15 x+25 y+12 x-72 y = (15 x+12 x)+(25 y-72 y):\)
\(\frac{(15 x+12 x)+(25 y-72 y)}{30}\)
Combine like terms in \(25 y-72 y.\)
\(25 y-72 y = -47 y:\)
\(\frac{-47 y+(15 x+12 x)}{30}\)
Add like terms in 15 x+12 x.
\(15 x+12 x = 27 x:\)

Answer 6

Refresh the page if you can't see certain signs.

Answer 7

a. 3x + 4y
b. \[\frac{ 9 }{ 10 }x-\frac{ 19 }{ 6}y\]
c. \[\frac{ 2 }{ 3 }y+14x\]
d. 32x+46y