Solve for x
x>\frac{16}{15}
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2\left(3x-1\right)-3\left(x-2\right)\times 1>4\left(5-3x\right)
Multiply both sides of the equation by 8, the least common multiple of 4,8,2. Since 8 is positive, the inequality direction remains the same.
6x-2-3\left(x-2\right)\times 1>4\left(5-3x\right)
Use the distributive property to multiply 2 by 3x-1.
6x-2-3\left(x-2\right)>4\left(5-3x\right)
Multiply 3 and 1 to get 3.
6x-2-3x+6>4\left(5-3x\right)
Use the distributive property to multiply -3 by x-2.
3x-2+6>4\left(5-3x\right)
Combine 6x and -3x to get 3x.
3x+4>4\left(5-3x\right)
Add -2 and 6 to get 4.
3x+4>20-12x
Use the distributive property to multiply 4 by 5-3x.
3x+4+12x>20
Add 12x to both sides.
15x+4>20
Combine 3x and 12x to get 15x.
15x>20-4
Subtract 4 from both sides.
15x>16
Subtract 4 from 20 to get 16.
x>\frac{16}{15}
Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.
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}