Solve 2(x+3)leq3(2x-1)

$$2 ( x + 3 ) \leq 3 ( 2 x - 1 )$$

Solve for x

$$x\geq \frac{9}{4}$$

Solution Steps

Use the distributive property to multiply 2 by x+3.

$$2x+6\leq 3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$2x+6\leq 6x-3$$

Subtract 6x from both sides.

$$2x+6-6x\leq -3$$

Combine 2x and -6x to get -4x.

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

Subtract 6 from both sides.

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

Subtract 6 from -3 to get -9.

$$-4x\leq -9$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\geq \frac{-9}{-4}$$

Fraction \frac{-9}{-4} can be simplified to \frac{9}{4} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{9}{4}$$