Solve for x
x>\frac{20}{7}
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\frac{3}{2}x+\frac{3}{2}\left(-2\right)+1>-2\left(x-4\right)
Use the distributive property to multiply \frac{3}{2} by x-2.
\frac{3}{2}x+\frac{3\left(-2\right)}{2}+1>-2\left(x-4\right)
Express \frac{3}{2}\left(-2\right) as a single fraction.
\frac{3}{2}x+\frac{-6}{2}+1>-2\left(x-4\right)
Multiply 3 and -2 to get -6.
\frac{3}{2}x-3+1>-2\left(x-4\right)
Divide -6 by 2 to get -3.
\frac{3}{2}x-2>-2\left(x-4\right)
Add -3 and 1 to get -2.
\frac{3}{2}x-2>-2x+8
Use the distributive property to multiply -2 by x-4.
\frac{3}{2}x-2+2x>8
Add 2x to both sides.
\frac{7}{2}x-2>8
Combine \frac{3}{2}x and 2x to get \frac{7}{2}x.
\frac{7}{2}x>8+2
Add 2 to both sides.
\frac{7}{2}x>10
Add 8 and 2 to get 10.
x>10\times \frac{2}{7}
Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}. Since \frac{7}{2} is positive, the inequality direction remains the same.
x>\frac{10\times 2}{7}
Express 10\times \frac{2}{7} as a single fraction.
x>\frac{20}{7}
Multiply 10 and 2 to get 20.
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}