Solve for x
x=\frac{1}{3}\approx 0.333333333
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3\left(2x+8\right)-5\left(x-4\right)=3x-2+x+3\left(12x+11\right)
Multiply both sides of the equation by 15, the least common multiple of 5,3,15.
6x+24-5\left(x-4\right)=3x-2+x+3\left(12x+11\right)
Use the distributive property to multiply 3 by 2x+8.
6x+24-5x+20=3x-2+x+3\left(12x+11\right)
Use the distributive property to multiply -5 by x-4.
x+24+20=3x-2+x+3\left(12x+11\right)
Combine 6x and -5x to get x.
x+44=3x-2+x+3\left(12x+11\right)
Add 24 and 20 to get 44.
x+44=4x-2+3\left(12x+11\right)
Combine 3x and x to get 4x.
x+44=4x-2+36x+33
Use the distributive property to multiply 3 by 12x+11.
x+44=40x-2+33
Combine 4x and 36x to get 40x.
x+44=40x+31
Add -2 and 33 to get 31.
x+44-40x=31
Subtract 40x from both sides.
-39x+44=31
Combine x and -40x to get -39x.
-39x=31-44
Subtract 44 from both sides.
-39x=-13
Subtract 44 from 31 to get -13.
x=\frac{-13}{-39}
Divide both sides by -39.
x=\frac{1}{3}
Reduce the fraction \frac{-13}{-39} to lowest terms by extracting and canceling out -13.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}