Solve for x
x\in \left(-\frac{2}{3},4\right)
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3x+2>0 3x+2<0
Denominator 3x+2 cannot be zero since division by zero is not defined. There are two cases.
3x>-2
Consider the case when 3x+2 is positive. Move 2 to the right hand side.
x>-\frac{2}{3}
Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.
7x<2\left(3x+2\right)
The initial inequality does not change the direction when multiplied by 3x+2 for 3x+2>0.
7x<6x+4
Multiply out the right hand side.
7x-6x<4
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(-\frac{2}{3},4\right)
Consider condition x>-\frac{2}{3} specified above.
3x<-2
Now consider the case when 3x+2 is negative. Move 2 to the right hand side.
x<-\frac{2}{3}
Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.
7x>2\left(3x+2\right)
The initial inequality changes the direction when multiplied by 3x+2 for 3x+2<0.
7x>6x+4
Multiply out the right hand side.
7x-6x>4
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<-\frac{2}{3} specified above.
x\in \left(-\frac{2}{3},4\right)
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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y = 3x + 4
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699 * 533
Matrix
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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}