Solve 6+5x/4geq3(x-3)

$$\frac { 6 + 5 x } { 4 } \geq 3 ( x - 3 )$$

Solve for x

$$x\leq 6$$

Solution Steps

Multiply both sides of the equation by 4. Since 4 is positive, the inequality direction remains the same.

$$6+5x\geq 12\left(x-3\right)$$

Use the distributive property to multiply 12 by x-3.

$$6+5x\geq 12x-36$$

Subtract 12x from both sides.

$$6+5x-12x\geq -36$$

Combine 5x and -12x to get -7x.

$$6-7x\geq -36$$

Subtract 6 from both sides.

$$-7x\geq -36-6$$

Subtract 6 from -36 to get -42.

$$-7x\geq -42$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\leq \frac{-42}{-7}$$

Divide -42 by -7 to get 6.

$$x\leq 6$$