Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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-5\left(x+2\right)-30\left(\frac{x}{2}-2\right)=-20\left(x-\frac{5}{2}\right)
Multiply both sides of the equation by 10, the least common multiple of 2,5.
-5x-10-30\left(\frac{x}{2}-2\right)=-20\left(x-\frac{5}{2}\right)
Use the distributive property to multiply -5 by x+2.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x-20\left(-\frac{5}{2}\right)
Use the distributive property to multiply -20 by x-\frac{5}{2}.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+\frac{-20\left(-5\right)}{2}
Express -20\left(-\frac{5}{2}\right) as a single fraction.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+\frac{100}{2}
Multiply -20 and -5 to get 100.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+50
Divide 100 by 2 to get 50.
-5x-10-30\left(\frac{x}{2}-2\right)+20x=50
Add 20x to both sides.
2\left(-5x-10-30\left(\frac{x}{2}-2\right)\right)+40x=100
Multiply both sides of the equation by 2.
4\left(-5x-10-30\left(\frac{x}{2}-2\right)\right)+80x=200
Multiply both sides of the equation by 2.
4\left(-5x-10-30\times \frac{x}{2}+60\right)+80x=200
Use the distributive property to multiply -30 by \frac{x}{2}-2.
4\left(-5x-10-15x+60\right)+80x=200
Cancel out 2, the greatest common factor in 30 and 2.
4\left(-20x-10+60\right)+80x=200
Combine -5x and -15x to get -20x.
4\left(-20x+50\right)+80x=200
Add -10 and 60 to get 50.
-80x+200+80x=200
Use the distributive property to multiply 4 by -20x+50.
200=200
Combine -80x and 80x to get 0.
\text{true}
Compare 200 and 200.
x\in \mathrm{C}
This is true for any x.
-5\left(x+2\right)-30\left(\frac{x}{2}-2\right)=-20\left(x-\frac{5}{2}\right)
Multiply both sides of the equation by 10, the least common multiple of 2,5.
-5x-10-30\left(\frac{x}{2}-2\right)=-20\left(x-\frac{5}{2}\right)
Use the distributive property to multiply -5 by x+2.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x-20\left(-\frac{5}{2}\right)
Use the distributive property to multiply -20 by x-\frac{5}{2}.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+\frac{-20\left(-5\right)}{2}
Express -20\left(-\frac{5}{2}\right) as a single fraction.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+\frac{100}{2}
Multiply -20 and -5 to get 100.
-5x-10-30\left(\frac{x}{2}-2\right)=-20x+50
Divide 100 by 2 to get 50.
-5x-10-30\left(\frac{x}{2}-2\right)+20x=50
Add 20x to both sides.
2\left(-5x-10-30\left(\frac{x}{2}-2\right)\right)+40x=100
Multiply both sides of the equation by 2.
4\left(-5x-10-30\left(\frac{x}{2}-2\right)\right)+80x=200
Multiply both sides of the equation by 2.
4\left(-5x-10-30\times \frac{x}{2}+60\right)+80x=200
Use the distributive property to multiply -30 by \frac{x}{2}-2.
4\left(-5x-10-15x+60\right)+80x=200
Cancel out 2, the greatest common factor in 30 and 2.
4\left(-20x-10+60\right)+80x=200
Combine -5x and -15x to get -20x.
4\left(-20x+50\right)+80x=200
Add -10 and 60 to get 50.
-80x+200+80x=200
Use the distributive property to multiply 4 by -20x+50.
200=200
Combine -80x and 80x to get 0.
\text{true}
Compare 200 and 200.
x\in \mathrm{R}
This is true for any x.
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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
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