Solve for x
x\in (-\infty,-4]\cup (-1,\infty)
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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+5\geq x+1
The initial inequality does not change the direction when multiplied by x+1 for x+1>0.
2x-x\geq -5+1
Move the terms containing x to the left hand side and all other terms to the right hand side.
x\geq -4
Combine like terms.
x>-1
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+5\leq x+1
The initial inequality changes the direction when multiplied by x+1 for x+1<0.
2x-x\leq -5+1
Move the terms containing x to the left hand side and all other terms to the right hand side.
x\leq -4
Combine like terms.
x\in (-\infty,-4]\cup (-1,\infty)
The final solution is the union of the obtained solutions.
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