Solve for x
x<5
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2\times 7x-11\left(x+1\right)>2\left(3x-1\right)-3\left(13-x\right)
Multiply both sides of the equation by 6, the least common multiple of 3,6,2. Since 6 is positive, the inequality direction remains the same.
14x-11\left(x+1\right)>2\left(3x-1\right)-3\left(13-x\right)
Multiply 2 and 7 to get 14.
14x-11x-11>2\left(3x-1\right)-3\left(13-x\right)
Use the distributive property to multiply -11 by x+1.
3x-11>2\left(3x-1\right)-3\left(13-x\right)
Combine 14x and -11x to get 3x.
3x-11>6x-2-3\left(13-x\right)
Use the distributive property to multiply 2 by 3x-1.
3x-11>6x-2-39+3x
Use the distributive property to multiply -3 by 13-x.
3x-11>6x-41+3x
Subtract 39 from -2 to get -41.
3x-11>9x-41
Combine 6x and 3x to get 9x.
3x-11-9x>-41
Subtract 9x from both sides.
-6x-11>-41
Combine 3x and -9x to get -6x.
-6x>-41+11
Add 11 to both sides.
-6x>-30
Add -41 and 11 to get -30.
x<\frac{-30}{-6}
Divide both sides by -6. Since -6 is negative, the inequality direction is changed.
x<5
Divide -30 by -6 to get 5.
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}