Solve 3+x/2-1leq4x+3/6

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

Solve for x

$$x\geq 0$$

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.

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

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

$$9+3x-6\leq 4x+3$$

Subtract 6 from 9 to get 3.

$$3+3x\leq 4x+3$$

Subtract 4x from both sides.

$$3+3x-4x\leq 3$$

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

$$3-x\leq 3$$

Subtract 3 from both sides.

$$-x\leq 3-3$$

Subtract 3 from 3 to get 0.

$$-x\leq 0$$

Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since -1\leq 0, x must be ≥0.

$$x\geq 0$$