Solve for x
x>\frac{9}{8}
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6\left(x+1\right)-4\left(3-x\right)>-4x+3\left(2x+1\right)
Multiply both sides of the equation by 12, the least common multiple of 2,3,4. Since 12 is positive, the inequality direction remains the same.
6x+6-4\left(3-x\right)>-4x+3\left(2x+1\right)
Use the distributive property to multiply 6 by x+1.
6x+6-12+4x>-4x+3\left(2x+1\right)
Use the distributive property to multiply -4 by 3-x.
6x-6+4x>-4x+3\left(2x+1\right)
Subtract 12 from 6 to get -6.
10x-6>-4x+3\left(2x+1\right)
Combine 6x and 4x to get 10x.
10x-6>-4x+6x+3
Use the distributive property to multiply 3 by 2x+1.
10x-6>2x+3
Combine -4x and 6x to get 2x.
10x-6-2x>3
Subtract 2x from both sides.
8x-6>3
Combine 10x and -2x to get 8x.
8x>3+6
Add 6 to both sides.
8x>9
Add 3 and 6 to get 9.
x>\frac{9}{8}
Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.
Examples
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{ 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}