Solve x/4-2/3geq4x-3/2

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

Solve for x

$$x\leq \frac{10}{21}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3,2. Since 12 is positive, the inequality direction remains the same.

$$3x-8\geq 6\left(4x-3\right)$$

Use the distributive property to multiply 6 by 4x-3.

$$3x-8\geq 24x-18$$

Subtract 24x from both sides.

$$3x-8-24x\geq -18$$

Combine 3x and -24x to get -21x.

$$-21x-8\geq -18$$

Add 8 to both sides.

$$-21x\geq -18+8$$

Add -18 and 8 to get -10.

$$-21x\geq -10$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$x\leq \frac{-10}{-21}$$

Fraction \frac{-10}{-21} can be simplified to \frac{10}{21} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{10}{21}$$