Solve 15-x/3leq4x+1/2

$$\frac { 15 - x } { 3 } \leq \frac { 4 x + 1 } { 2 }$$

Solve for x

$$x\geq \frac{27}{14}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(15-x\right)\leq 3\left(4x+1\right)$$

Use the distributive property to multiply 2 by 15-x.

$$30-2x\leq 3\left(4x+1\right)$$

Use the distributive property to multiply 3 by 4x+1.

$$30-2x\leq 12x+3$$

Subtract 12x from both sides.

$$30-2x-12x\leq 3$$

Combine -2x and -12x to get -14x.

$$30-14x\leq 3$$

Subtract 30 from both sides.

$$-14x\leq 3-30$$

Subtract 30 from 3 to get -27.

$$-14x\leq -27$$

Divide both sides by -14. Since -14 is negative, the inequality direction is changed.

$$x\geq \frac{-27}{-14}$$

Fraction \frac{-27}{-14} can be simplified to \frac{27}{14} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{27}{14}$$