Solve for x
x<-1
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3\left(3x+5\right)+12x<2\left(2x-1\right)
Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.
9x+15+12x<2\left(2x-1\right)
Use the distributive property to multiply 3 by 3x+5.
21x+15<2\left(2x-1\right)
Combine 9x and 12x to get 21x.
21x+15<4x-2
Use the distributive property to multiply 2 by 2x-1.
21x+15-4x<-2
Subtract 4x from both sides.
17x+15<-2
Combine 21x and -4x to get 17x.
17x<-2-15
Subtract 15 from both sides.
17x<-17
Subtract 15 from -2 to get -17.
x<\frac{-17}{17}
Divide both sides by 17. Since 17 is positive, the inequality direction remains the same.
x<-1
Divide -17 by 17 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}