Solve 3*x-4/2+3geqx

$$3 \cdot \frac { x - 4 } { 2 } + 3 \geq x$$

Solve for x

$$x\geq 6$$

Solution Steps

Express 3\times \frac{x-4}{2} as a single fraction.

$$\frac{3\left(x-4\right)}{2}+3\geq x$$

Use the distributive property to multiply 3 by x-4.

$$\frac{3x-12}{2}+3\geq x$$

Divide each term of 3x-12 by 2 to get \frac{3}{2}x-6.

$$\frac{3}{2}x-6+3\geq x$$

Add -6 and 3 to get -3.

$$\frac{3}{2}x-3\geq x$$

Subtract x from both sides.

$$\frac{3}{2}x-3-x\geq 0$$

Combine \frac{3}{2}x and -x to get \frac{1}{2}x.

$$\frac{1}{2}x-3\geq 0$$

Add 3 to both sides. Anything plus zero gives itself.

$$\frac{1}{2}x\geq 3$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$x\geq 3\times 2$$

Multiply 3 and 2 to get 6.

$$x\geq 6$$