Solve for x
x\in \mathrm{R}
y<0
Solve for y
y<0
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x-\frac{y}{2}-x>0
Subtract x from both sides.
-\frac{y}{2}>0
Combine x and -x to get 0.
-y>0
Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.
y<0
Product of two numbers is >0 if both are >0 or both are <0. Since -1<0, y must be <0.
-\frac{y}{2}>x-x
Subtract x from both sides.
-\frac{y}{2}>0
Combine x and -x to get 0.
-y>0
Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.
y<0
Product of two numbers is >0 if both are >0 or both are <0. Since -1<0, y must be <0.
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}