Solve 3x/5+1/2geq5x/6+1/3

$$\frac { 3 x } { 5 } + \frac { 1 } { 2 } \geq \frac { 5 x } { 6 } + \frac { 1 } { 3 }$$

Solve for x

$$x\leq \frac{5}{7}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,2,6,3. Since 30 is positive, the inequality direction remains the same.

$$6\times 3x+15\geq 5\times 5x+10$$

Multiply 6 and 3 to get 18.

$$18x+15\geq 5\times 5x+10$$

Multiply 5 and 5 to get 25.

$$18x+15\geq 25x+10$$

Subtract 25x from both sides.

$$18x+15-25x\geq 10$$

Combine 18x and -25x to get -7x.

$$-7x+15\geq 10$$

Subtract 15 from both sides.

$$-7x\geq 10-15$$

Subtract 15 from 10 to get -5.

$$-7x\geq -5$$

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

$$x\leq \frac{-5}{-7}$$

Fraction \frac{-5}{-7} can be simplified to \frac{5}{7} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{5}{7}$$