Solve for x
x>-\frac{3}{8}
Graph
Share
Copied to clipboard
6\left(2x-3\right)+5\left(9-4x\right)<30
Multiply both sides of the equation by 30, the least common multiple of 5,6. Since 30 is positive, the inequality direction remains the same.
12x-18+5\left(9-4x\right)<30
Use the distributive property to multiply 6 by 2x-3.
12x-18+45-20x<30
Use the distributive property to multiply 5 by 9-4x.
12x+27-20x<30
Add -18 and 45 to get 27.
-8x+27<30
Combine 12x and -20x to get -8x.
-8x<30-27
Subtract 27 from both sides.
-8x<3
Subtract 27 from 30 to get 3.
x>-\frac{3}{8}
Divide both sides by -8. Since -8 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}