Solve for x
x\leq 4
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3\left(3x-2\right)\geq 5\left(2x+1\right)-15
Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.
9x-6\geq 5\left(2x+1\right)-15
Use the distributive property to multiply 3 by 3x-2.
9x-6\geq 10x+5-15
Use the distributive property to multiply 5 by 2x+1.
9x-6\geq 10x-10
Subtract 15 from 5 to get -10.
9x-6-10x\geq -10
Subtract 10x from both sides.
-x-6\geq -10
Combine 9x and -10x to get -x.
-x\geq -10+6
Add 6 to both sides.
-x\geq -4
Add -10 and 6 to get -4.
x\leq \frac{-4}{-1}
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
x\leq 4
Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.
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}