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\frac{147x-177}{5}
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\frac{147x-177}{5}
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45x-30-7\left(2x-1\right)-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Use the distributive property to multiply 15 by 3x-2.
45x-30-14x+7-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Use the distributive property to multiply -7 by 2x-1.
31x-30+7-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Combine 45x and -14x to get 31x.
31x-23-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Add -30 and 7 to get -23.
31x-23-\left(\frac{14}{5}\left(2x+3\right)-4\left(x-1\right)\right)
Anything divided by one gives itself.
31x-23-\left(\frac{14}{5}\times 2x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Use the distributive property to multiply \frac{14}{5} by 2x+3.
31x-23-\left(\frac{14\times 2}{5}x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Express \frac{14}{5}\times 2 as a single fraction.
31x-23-\left(\frac{28}{5}x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Multiply 14 and 2 to get 28.
31x-23-\left(\frac{28}{5}x+\frac{14\times 3}{5}-4\left(x-1\right)\right)
Express \frac{14}{5}\times 3 as a single fraction.
31x-23-\left(\frac{28}{5}x+\frac{42}{5}-4\left(x-1\right)\right)
Multiply 14 and 3 to get 42.
31x-23-\left(\frac{28}{5}x+\frac{42}{5}-4x+4\right)
Use the distributive property to multiply -4 by x-1.
31x-23-\left(\frac{8}{5}x+\frac{42}{5}+4\right)
Combine \frac{28}{5}x and -4x to get \frac{8}{5}x.
31x-23-\left(\frac{8}{5}x+\frac{42}{5}+\frac{20}{5}\right)
Convert 4 to fraction \frac{20}{5}.
31x-23-\left(\frac{8}{5}x+\frac{42+20}{5}\right)
Since \frac{42}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.
31x-23-\left(\frac{8}{5}x+\frac{62}{5}\right)
Add 42 and 20 to get 62.
31x-23-\frac{8}{5}x-\frac{62}{5}
To find the opposite of \frac{8}{5}x+\frac{62}{5}, find the opposite of each term.
\frac{147}{5}x-23-\frac{62}{5}
Combine 31x and -\frac{8}{5}x to get \frac{147}{5}x.
\frac{147}{5}x-\frac{115}{5}-\frac{62}{5}
Convert -23 to fraction -\frac{115}{5}.
\frac{147}{5}x+\frac{-115-62}{5}
Since -\frac{115}{5} and \frac{62}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{147}{5}x-\frac{177}{5}
Subtract 62 from -115 to get -177.
45x-30-7\left(2x-1\right)-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Use the distributive property to multiply 15 by 3x-2.
45x-30-14x+7-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Use the distributive property to multiply -7 by 2x-1.
31x-30+7-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Combine 45x and -14x to get 31x.
31x-23-\left(\frac{14}{5}\left(\frac{2}{1}x+3\right)-4\left(x-1\right)\right)
Add -30 and 7 to get -23.
31x-23-\left(\frac{14}{5}\left(2x+3\right)-4\left(x-1\right)\right)
Anything divided by one gives itself.
31x-23-\left(\frac{14}{5}\times 2x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Use the distributive property to multiply \frac{14}{5} by 2x+3.
31x-23-\left(\frac{14\times 2}{5}x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Express \frac{14}{5}\times 2 as a single fraction.
31x-23-\left(\frac{28}{5}x+\frac{14}{5}\times 3-4\left(x-1\right)\right)
Multiply 14 and 2 to get 28.
31x-23-\left(\frac{28}{5}x+\frac{14\times 3}{5}-4\left(x-1\right)\right)
Express \frac{14}{5}\times 3 as a single fraction.
31x-23-\left(\frac{28}{5}x+\frac{42}{5}-4\left(x-1\right)\right)
Multiply 14 and 3 to get 42.
31x-23-\left(\frac{28}{5}x+\frac{42}{5}-4x+4\right)
Use the distributive property to multiply -4 by x-1.
31x-23-\left(\frac{8}{5}x+\frac{42}{5}+4\right)
Combine \frac{28}{5}x and -4x to get \frac{8}{5}x.
31x-23-\left(\frac{8}{5}x+\frac{42}{5}+\frac{20}{5}\right)
Convert 4 to fraction \frac{20}{5}.
31x-23-\left(\frac{8}{5}x+\frac{42+20}{5}\right)
Since \frac{42}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.
31x-23-\left(\frac{8}{5}x+\frac{62}{5}\right)
Add 42 and 20 to get 62.
31x-23-\frac{8}{5}x-\frac{62}{5}
To find the opposite of \frac{8}{5}x+\frac{62}{5}, find the opposite of each term.
\frac{147}{5}x-23-\frac{62}{5}
Combine 31x and -\frac{8}{5}x to get \frac{147}{5}x.
\frac{147}{5}x-\frac{115}{5}-\frac{62}{5}
Convert -23 to fraction -\frac{115}{5}.
\frac{147}{5}x+\frac{-115-62}{5}
Since -\frac{115}{5} and \frac{62}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{147}{5}x-\frac{177}{5}
Subtract 62 from -115 to get -177.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}