Solve for x
x\leq 17
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12x-3\left(x-1\right)-2\left(2x-4\right)\geq 6x-6
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.
12x-3x+3-2\left(2x-4\right)\geq 6x-6
Use the distributive property to multiply -3 by x-1.
9x+3-2\left(2x-4\right)\geq 6x-6
Combine 12x and -3x to get 9x.
9x+3-4x+8\geq 6x-6
Use the distributive property to multiply -2 by 2x-4.
5x+3+8\geq 6x-6
Combine 9x and -4x to get 5x.
5x+11\geq 6x-6
Add 3 and 8 to get 11.
5x+11-6x\geq -6
Subtract 6x from both sides.
-x+11\geq -6
Combine 5x and -6x to get -x.
-x\geq -6-11
Subtract 11 from both sides.
-x\geq -17
Subtract 11 from -6 to get -17.
x\leq \frac{-17}{-1}
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
x\leq 17
Fraction \frac{-17}{-1} can be simplified to 17 by removing the negative sign from both the numerator and the denominator.
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}