[ \frac { 3 x } { 2 } + \frac { 2 x } { 3 } = \frac { 1 + 3 x } { 2 } ]
Solve for x
x=\frac{3}{4}=0.75
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3\times 3x+2\times 2x=3\left(1+3x\right)
Multiply both sides of the equation by 6, the least common multiple of 2,3.
9x+2\times 2x=3\left(1+3x\right)
Multiply 3 and 3 to get 9.
9x+4x=3\left(1+3x\right)
Multiply 2 and 2 to get 4.
13x=3\left(1+3x\right)
Combine 9x and 4x to get 13x.
13x=3+9x
Use the distributive property to multiply 3 by 1+3x.
13x-9x=3
Subtract 9x from both sides.
4x=3
Combine 13x and -9x to get 4x.
x=\frac{3}{4}
Divide both sides by 4.
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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Matrix
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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}