Solve for x
x\geq -\frac{12}{5}
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3\left(x+2\right)\geq -2\left(x+3\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.
3x+6\geq -2\left(x+3\right)
Use the distributive property to multiply 3 by x+2.
3x+6\geq -2x-6
Use the distributive property to multiply -2 by x+3.
3x+6+2x\geq -6
Add 2x to both sides.
5x+6\geq -6
Combine 3x and 2x to get 5x.
5x\geq -6-6
Subtract 6 from both sides.
5x\geq -12
Subtract 6 from -6 to get -12.
x\geq -\frac{12}{5}
Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.
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}