Solve for x
x\geq \frac{7}{2}
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2\left(3x+2\right)\leq 5\left(2x-2\right)
Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.
6x+4\leq 5\left(2x-2\right)
Use the distributive property to multiply 2 by 3x+2.
6x+4\leq 10x-10
Use the distributive property to multiply 5 by 2x-2.
6x+4-10x\leq -10
Subtract 10x from both sides.
-4x+4\leq -10
Combine 6x and -10x to get -4x.
-4x\leq -10-4
Subtract 4 from both sides.
-4x\leq -14
Subtract 4 from -10 to get -14.
x\geq \frac{-14}{-4}
Divide both sides by -4. Since -4 is negative, the inequality direction is changed.
x\geq \frac{7}{2}
Reduce the fraction \frac{-14}{-4} to lowest terms by extracting and canceling out -2.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}