Solve for x
x\in [-8,1)
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x-1>0 x-1<0
Denominator x-1 cannot be zero since division by zero is not defined. There are two cases.
x>1
Consider the case when x-1 is positive. Move -1 to the right hand side.
2x+7\leq x-1
The initial inequality does not change the direction when multiplied by x-1 for x-1>0.
2x-x\leq -7-1
Move the terms containing x to the left hand side and all other terms to the right hand side.
x\leq -8
Combine like terms.
x\in \emptyset
Consider condition x>1 specified above.
x<1
Now consider the case when x-1 is negative. Move -1 to the right hand side.
2x+7\geq x-1
The initial inequality changes the direction when multiplied by x-1 for x-1<0.
2x-x\geq -7-1
Move the terms containing x to the left hand side and all other terms to the right hand side.
x\geq -8
Combine like terms.
x\in [-8,1)
Consider condition x<1 specified above.
x\in [-8,1)
The final solution is the union of the obtained solutions.
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Limits
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