Solve for x
x<2
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12\left(x+1\right)-2\left(x-2\right)>3\left(7x-2\right)
Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.
12x+12-2\left(x-2\right)>3\left(7x-2\right)
Use the distributive property to multiply 12 by x+1.
12x+12-2x+4>3\left(7x-2\right)
Use the distributive property to multiply -2 by x-2.
10x+12+4>3\left(7x-2\right)
Combine 12x and -2x to get 10x.
10x+16>3\left(7x-2\right)
Add 12 and 4 to get 16.
10x+16>21x-6
Use the distributive property to multiply 3 by 7x-2.
10x+16-21x>-6
Subtract 21x from both sides.
-11x+16>-6
Combine 10x and -21x to get -11x.
-11x>-6-16
Subtract 16 from both sides.
-11x>-22
Subtract 16 from -6 to get -22.
x<\frac{-22}{-11}
Divide both sides by -11. Since -11 is negative, the inequality direction is changed.
x<2
Divide -22 by -11 to get 2.
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Limits
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