Solve for x
x>3
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4\left(8x-6\right)-6\left(7x-5\right)<24-3\left(3x+7\right)
Multiply both sides of the equation by 12, the least common multiple of 3,2,4. Since 12 is positive, the inequality direction remains the same.
32x-24-6\left(7x-5\right)<24-3\left(3x+7\right)
Use the distributive property to multiply 4 by 8x-6.
32x-24-42x+30<24-3\left(3x+7\right)
Use the distributive property to multiply -6 by 7x-5.
-10x-24+30<24-3\left(3x+7\right)
Combine 32x and -42x to get -10x.
-10x+6<24-3\left(3x+7\right)
Add -24 and 30 to get 6.
-10x+6<24-9x-21
Use the distributive property to multiply -3 by 3x+7.
-10x+6<3-9x
Subtract 21 from 24 to get 3.
-10x+6+9x<3
Add 9x to both sides.
-x+6<3
Combine -10x and 9x to get -x.
-x<3-6
Subtract 6 from both sides.
-x<-3
Subtract 6 from 3 to get -3.
x>\frac{-3}{-1}
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
x>3
Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.
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}