Solve for x
x>3
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x-3>0 x-3<0
Denominator x-3 cannot be zero since division by zero is not defined. There are two cases.
x>3
Consider the case when x-3 is positive. Move -3 to the right hand side.
x+1\geq x-3
The initial inequality does not change the direction when multiplied by x-3 for x-3>0.
x-x\geq -1-3
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\geq -4
Combine like terms.
x>3
Consider condition x>3 specified above.
x<3
Now consider the case when x-3 is negative. Move -3 to the right hand side.
x+1\leq x-3
The initial inequality changes the direction when multiplied by x-3 for x-3<0.
x-x\leq -1-3
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\leq -4
Combine like terms.
x\in \emptyset
Consider condition x<3 specified above.
x>3
The final solution is the union of the obtained solutions.
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Linear equation
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Matrix
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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