Solve -7/2leq4/3-3x/5

$$- \frac { 7 } { 2 } \leq \frac { 4 } { 3 } - \frac { 3 x } { 5 }$$

Solve for x

$$x\leq \frac{145}{18}$$

Solution Steps

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

$$-105\leq 40-6\times 3x$$

Multiply -6 and 3 to get -18.

$$-105\leq 40-18x$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$40-18x\geq -105$$

Subtract 40 from both sides.

$$-18x\geq -105-40$$

Subtract 40 from -105 to get -145.

$$-18x\geq -145$$

Divide both sides by -18. Since -18 is negative, the inequality direction is changed.

$$x\leq \frac{-145}{-18}$$

Fraction \frac{-145}{-18} can be simplified to \frac{145}{18} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{145}{18}$$