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24x-36y-17z
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24x-36y-17z
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-15y-16z-\left(-12x\right)-\left(-13x+20y\right)-\left(x+y+z\right)
To find the opposite of 15y+16z-12x, find the opposite of each term.
-15y-16z+12x-\left(-13x+20y\right)-\left(x+y+z\right)
The opposite of -12x is 12x.
-15y-16z+12x-\left(-13x\right)-20y-\left(x+y+z\right)
To find the opposite of -13x+20y, find the opposite of each term.
-15y-16z+12x+13x-20y-\left(x+y+z\right)
The opposite of -13x is 13x.
-15y-16z+25x-20y-\left(x+y+z\right)
Combine 12x and 13x to get 25x.
-35y-16z+25x-\left(x+y+z\right)
Combine -15y and -20y to get -35y.
-35y-16z+25x-x-y-z
To find the opposite of x+y+z, find the opposite of each term.
-35y-16z+24x-y-z
Combine 25x and -x to get 24x.
-36y-16z+24x-z
Combine -35y and -y to get -36y.
-36y-17z+24x
Combine -16z and -z to get -17z.
-15y-16z-\left(-12x\right)-\left(-13x+20y\right)-\left(x+y+z\right)
To find the opposite of 15y+16z-12x, find the opposite of each term.
-15y-16z+12x-\left(-13x+20y\right)-\left(x+y+z\right)
The opposite of -12x is 12x.
-15y-16z+12x-\left(-13x\right)-20y-\left(x+y+z\right)
To find the opposite of -13x+20y, find the opposite of each term.
-15y-16z+12x+13x-20y-\left(x+y+z\right)
The opposite of -13x is 13x.
-15y-16z+25x-20y-\left(x+y+z\right)
Combine 12x and 13x to get 25x.
-35y-16z+25x-\left(x+y+z\right)
Combine -15y and -20y to get -35y.
-35y-16z+25x-x-y-z
To find the opposite of x+y+z, find the opposite of each term.
-35y-16z+24x-y-z
Combine 25x and -x to get 24x.
-36y-16z+24x-z
Combine -35y and -y to get -36y.
-36y-17z+24x
Combine -16z and -z to get -17z.
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\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}