Solve for x
x=-2
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5\left(x-2\right)-4\left(x-3\right)=5\left(x+2\right)
Multiply both sides of the equation by 20, the least common multiple of 4,5.
5x-10-4\left(x-3\right)=5\left(x+2\right)
Use the distributive property to multiply 5 by x-2.
5x-10-4x+12=5\left(x+2\right)
Use the distributive property to multiply -4 by x-3.
x-10+12=5\left(x+2\right)
Combine 5x and -4x to get x.
x+2=5\left(x+2\right)
Add -10 and 12 to get 2.
x+2=5x+10
Use the distributive property to multiply 5 by x+2.
x+2-5x=10
Subtract 5x from both sides.
-4x+2=10
Combine x and -5x to get -4x.
-4x=10-2
Subtract 2 from both sides.
-4x=8
Subtract 2 from 10 to get 8.
x=\frac{8}{-4}
Divide both sides by -4.
x=-2
Divide 8 by -4 to get -2.
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}