Solve -1/2leq4/5-3x/5

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

Solve for x

$$x\leq \frac{13}{6}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$-5\leq 8-2\times 3x$$

Multiply -2 and 3 to get -6.

$$-5\leq 8-6x$$

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

$$8-6x\geq -5$$

Subtract 8 from both sides.

$$-6x\geq -5-8$$

Subtract 8 from -5 to get -13.

$$-6x\geq -13$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\leq \frac{-13}{-6}$$

Fraction \frac{-13}{-6} can be simplified to \frac{13}{6} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{13}{6}$$