Solve for x
x\in (-\infty,1)\cup [6,\infty)
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4x-4>0 4x-4<0
Denominator 4x-4 cannot be zero since division by zero is not defined. There are two cases.
4x>4
Consider the case when 4x-4 is positive. Move -4 to the right hand side.
x>1
Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.
3x+2\leq 4x-4
The initial inequality does not change the direction when multiplied by 4x-4 for 4x-4>0.
3x-4x\leq -2-4
Move the terms containing x to the left hand side and all other terms to the right hand side.
-x\leq -6
Combine like terms.
x\geq 6
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
4x<4
Now consider the case when 4x-4 is negative. Move -4 to the right hand side.
x<1
Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.
3x+2\geq 4x-4
The initial inequality changes the direction when multiplied by 4x-4 for 4x-4<0.
3x-4x\geq -2-4
Move the terms containing x to the left hand side and all other terms to the right hand side.
-x\geq -6
Combine like terms.
x\leq 6
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
x<1
Consider condition x<1 specified above.
x\in (-\infty,1)\cup [6,\infty)
The final solution is the union of the obtained solutions.
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Limits
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