Solve 3+x/2-1<4x+3/6

$$\frac { 3 + x } { 2 } - 1 < \frac { 4 x + 3 } { 6 }$$

Solve for x

$$x>0$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,6. Since 6 is positive, the inequality direction remains the same.

$$3\left(3+x\right)-6<4x+3$$

Use the distributive property to multiply 3 by 3+x.

$$9+3x-6<4x+3$$

Subtract 6 from 9 to get 3.

$$3+3x<4x+3$$

Subtract 4x from both sides.

$$3+3x-4x<3$$

Combine 3x and -4x to get -x.

$$3-x<3$$

Subtract 3 from both sides.

$$-x<3-3$$

Subtract 3 from 3 to get 0.

$$-x<0$$

Product of two numbers is <0 if one is >0 and the other is <0. Since -1<0, x must be >0.

$$x>0$$