Solve x/3leq1/4+3x-2/5

$$\frac { x } { 3 } \leq \frac { 1 } { 4 } + \frac { 3 x - 2 } { 5 }$$

Solve for x

$$x\geq \frac{9}{16}$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 3,4,5. Since 60 is positive, the inequality direction remains the same.

$$20x\leq 15+12\left(3x-2\right)$$

Use the distributive property to multiply 12 by 3x-2.

$$20x\leq 15+36x-24$$

Subtract 24 from 15 to get -9.

$$20x\leq -9+36x$$

Subtract 36x from both sides.

$$20x-36x\leq -9$$

Combine 20x and -36x to get -16x.

$$-16x\leq -9$$

Divide both sides by -16. Since -16 is negative, the inequality direction is changed.

$$x\geq \frac{-9}{-16}$$

Fraction \frac{-9}{-16} can be simplified to \frac{9}{16} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{9}{16}$$