Solve for x
x>-\frac{2}{5}
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5\left(2x-1\right)-3\left(5x-1\right)<0
Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.
10x-5-3\left(5x-1\right)<0
Use the distributive property to multiply 5 by 2x-1.
10x-5-15x+3<0
Use the distributive property to multiply -3 by 5x-1.
-5x-5+3<0
Combine 10x and -15x to get -5x.
-5x-2<0
Add -5 and 3 to get -2.
-5x<2
Add 2 to both sides. Anything plus zero gives itself.
x>-\frac{2}{5}
Divide both sides by -5. Since -5 is negative, the inequality direction is changed.
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}