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x=1
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5x-\frac{20}{4}-\frac{3}{4}+\frac{3}{4}x=2x-2
Convert -5 to fraction -\frac{20}{4}.
5x+\frac{-20-3}{4}+\frac{3}{4}x=2x-2
Since -\frac{20}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.
5x-\frac{23}{4}+\frac{3}{4}x=2x-2
Subtract 3 from -20 to get -23.
\frac{23}{4}x-\frac{23}{4}=2x-2
Combine 5x and \frac{3}{4}x to get \frac{23}{4}x.
\frac{23}{4}x-\frac{23}{4}-2x=-2
Subtract 2x from both sides.
\frac{15}{4}x-\frac{23}{4}=-2
Combine \frac{23}{4}x and -2x to get \frac{15}{4}x.
\frac{15}{4}x=-2+\frac{23}{4}
Add \frac{23}{4} to both sides.
\frac{15}{4}x=-\frac{8}{4}+\frac{23}{4}
Convert -2 to fraction -\frac{8}{4}.
\frac{15}{4}x=\frac{-8+23}{4}
Since -\frac{8}{4} and \frac{23}{4} have the same denominator, add them by adding their numerators.
\frac{15}{4}x=\frac{15}{4}
Add -8 and 23 to get 15.
x=\frac{15}{4}\times \frac{4}{15}
Multiply both sides by \frac{4}{15}, the reciprocal of \frac{15}{4}.
x=1
Cancel out \frac{15}{4} and its reciprocal \frac{4}{15}.
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}