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2\left(2x+1\right)-3x<6
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.
4x+2-3x<6
Use the distributive property to multiply 2 by 2x+1.
x+2<6
Combine 4x and -3x to get x.
x<6-2
Subtract 2 from both sides.
x<4
Subtract 2 from 6 to get 4.