Solve for x
x = \frac{8}{5} = 1\frac{3}{5} = 1.6
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2\left(x-4\right)=7\left(3x-2\right)+4x-42+14x-7x
Multiply both sides of the equation by 14, the least common multiple of 7,2.
2x-8=7\left(3x-2\right)+4x-42+14x-7x
Use the distributive property to multiply 2 by x-4.
2x-8=21x-14+4x-42+14x-7x
Use the distributive property to multiply 7 by 3x-2.
2x-8=25x-14-42+14x-7x
Combine 21x and 4x to get 25x.
2x-8=25x-56+14x-7x
Subtract 42 from -14 to get -56.
2x-8=39x-56-7x
Combine 25x and 14x to get 39x.
2x-8=32x-56
Combine 39x and -7x to get 32x.
2x-8-32x=-56
Subtract 32x from both sides.
-30x-8=-56
Combine 2x and -32x to get -30x.
-30x=-56+8
Add 8 to both sides.
-30x=-48
Add -56 and 8 to get -48.
x=\frac{-48}{-30}
Divide both sides by -30.
x=\frac{8}{5}
Reduce the fraction \frac{-48}{-30} to lowest terms by extracting and canceling out -6.
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}