Solve for x
x\geq -\frac{5}{2}
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3\left(2x-1\right)\geq 4\left(x-2\right)
Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.
6x-3\geq 4\left(x-2\right)
Use the distributive property to multiply 3 by 2x-1.
6x-3\geq 4x-8
Use the distributive property to multiply 4 by x-2.
6x-3-4x\geq -8
Subtract 4x from both sides.
2x-3\geq -8
Combine 6x and -4x to get 2x.
2x\geq -8+3
Add 3 to both sides.
2x\geq -5
Add -8 and 3 to get -5.
x\geq -\frac{5}{2}
Divide both sides by 2. Since 2 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}