Solve for x
x<7
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x-7>0 x-7<0
Denominator x-7 cannot be zero since division by zero is not defined. There are two cases.
x>7
Consider the case when x-7 is positive. Move -7 to the right hand side.
x+2\leq x-7
The initial inequality does not change the direction when multiplied by x-7 for x-7>0.
x-x\leq -2-7
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\leq -9
Combine like terms.
x\in \emptyset
Consider condition x>7 specified above.
x<7
Now consider the case when x-7 is negative. Move -7 to the right hand side.
x+2\geq x-7
The initial inequality changes the direction when multiplied by x-7 for x-7<0.
x-x\geq -2-7
Move the terms containing x to the left hand side and all other terms to the right hand side.
0\geq -9
Combine like terms.
x<7
Consider condition x<7 specified above.
x<7
The final solution is the union of the obtained solutions.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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