Solve for x
x>0
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-x-10+8x>3\left(x-4\right)-\left(x-2\right)
Subtract 2 from -8 to get -10.
-x-10+8x>3x-12-\left(x-2\right)
Use the distributive property to multiply 3 by x-4.
-x-10+8x>3x-12-x-\left(-2\right)
To find the opposite of x-2, find the opposite of each term.
-x-10+8x>3x-12-x+2
The opposite of -2 is 2.
-x-10+8x>2x-12+2
Combine 3x and -x to get 2x.
-x-10+8x>2x-10
Add -12 and 2 to get -10.
-x-10+8x-2x>-10
Subtract 2x from both sides.
-x-10+6x>-10
Combine 8x and -2x to get 6x.
-x+6x>-10+10
Add 10 to both sides.
-x+6x>0
Add -10 and 10 to get 0.
5x>0
Combine -x and 6x to get 5x.
x>0
Product of two numbers is >0 if both are >0 or both are <0. Since 5>0, x 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}