Solve for x
x\in \left(1,4\right)
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5x-5>0 5x-5<0
Denominator 5x-5 cannot be zero since division by zero is not defined. There are two cases.
5x>5
Consider the case when 5x-5 is positive. Move -5 to the right hand side.
x>1
Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.
4x-7<\frac{3}{5}\left(5x-5\right)
The initial inequality does not change the direction when multiplied by 5x-5 for 5x-5>0.
4x-7<3x-3
Multiply out the right hand side.
4x-3x<7-3
Move the terms containing x to the left hand side and all other terms to the right hand side.
x<4
Combine like terms.
x\in \left(1,4\right)
Consider condition x>1 specified above.
5x<5
Now consider the case when 5x-5 is negative. Move -5 to the right hand side.
x<1
Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.
4x-7>\frac{3}{5}\left(5x-5\right)
The initial inequality changes the direction when multiplied by 5x-5 for 5x-5<0.
4x-7>3x-3
Multiply out the right hand side.
4x-3x>7-3
Move the terms containing x to the left hand side and all other terms to the right hand side.
x>4
Combine like terms.
x\in \emptyset
Consider condition x<1 specified above.
x\in \left(1,4\right)
The final solution is the union of the obtained solutions.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}