Solve for x
x<3
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2\left(2x-3\right)<3\left(5-x\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.
4x-6<3\left(5-x\right)
Use the distributive property to multiply 2 by 2x-3.
4x-6<15-3x
Use the distributive property to multiply 3 by 5-x.
4x-6+3x<15
Add 3x to both sides.
7x-6<15
Combine 4x and 3x to get 7x.
7x<15+6
Add 6 to both sides.
7x<21
Add 15 and 6 to get 21.
x<\frac{21}{7}
Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.
x<3
Divide 21 by 7 to get 3.
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}