Solve for x
x<-1
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2\left(x-2\right)>3\left(3x+1\right)
Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.
2x-4>3\left(3x+1\right)
Use the distributive property to multiply 2 by x-2.
2x-4>9x+3
Use the distributive property to multiply 3 by 3x+1.
2x-4-9x>3
Subtract 9x from both sides.
-7x-4>3
Combine 2x and -9x to get -7x.
-7x>3+4
Add 4 to both sides.
-7x>7
Add 3 and 4 to get 7.
x<\frac{7}{-7}
Divide both sides by -7. Since -7 is negative, the inequality direction is changed.
x<-1
Divide 7 by -7 to get -1.
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}