Solve for k
k=-\frac{6x}{5}+4
Solve for x
x=-\frac{5k}{6}+\frac{10}{3}
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20-k\left(x+3\right)=6x-k\left(x-2\right)
Multiply both sides of the equation by 2.
20-\left(kx+3k\right)=6x-k\left(x-2\right)
Use the distributive property to multiply k by x+3.
20-kx-3k=6x-k\left(x-2\right)
To find the opposite of kx+3k, find the opposite of each term.
20-kx-3k=6x-\left(kx-2k\right)
Use the distributive property to multiply k by x-2.
20-kx-3k=6x-kx+2k
To find the opposite of kx-2k, find the opposite of each term.
20-kx-3k+kx=6x+2k
Add kx to both sides.
20-3k=6x+2k
Combine -kx and kx to get 0.
20-3k-2k=6x
Subtract 2k from both sides.
20-5k=6x
Combine -3k and -2k to get -5k.
-5k=6x-20
Subtract 20 from both sides.
\frac{-5k}{-5}=\frac{6x-20}{-5}
Divide both sides by -5.
k=\frac{6x-20}{-5}
Dividing by -5 undoes the multiplication by -5.
k=-\frac{6x}{5}+4
Divide 6x-20 by -5.
20-k\left(x+3\right)=6x-k\left(x-2\right)
Multiply both sides of the equation by 2.
20-\left(kx+3k\right)=6x-k\left(x-2\right)
Use the distributive property to multiply k by x+3.
20-kx-3k=6x-k\left(x-2\right)
To find the opposite of kx+3k, find the opposite of each term.
20-kx-3k=6x-\left(kx-2k\right)
Use the distributive property to multiply k by x-2.
20-kx-3k=6x-kx+2k
To find the opposite of kx-2k, find the opposite of each term.
20-kx-3k-6x=-kx+2k
Subtract 6x from both sides.
20-kx-3k-6x+kx=2k
Add kx to both sides.
20-3k-6x=2k
Combine -kx and kx to get 0.
-3k-6x=2k-20
Subtract 20 from both sides.
-6x=2k-20+3k
Add 3k to both sides.
-6x=5k-20
Combine 2k and 3k to get 5k.
\frac{-6x}{-6}=\frac{5k-20}{-6}
Divide both sides by -6.
x=\frac{5k-20}{-6}
Dividing by -6 undoes the multiplication by -6.
x=-\frac{5k}{6}+\frac{10}{3}
Divide -20+5k by -6.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}