Solve -x/3-2/5leq-2x-3/-3

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

Solve for x

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

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5,-3. Since 15 is positive, the inequality direction remains the same.

$$5\left(-x\right)-6\leq -5\left(-2x-3\right)$$

Use the distributive property to multiply -5 by -2x-3.

$$5\left(-x\right)-6\leq 10x+15$$

Subtract 10x from both sides.

$$5\left(-x\right)-6-10x\leq 15$$

Add 6 to both sides.

$$5\left(-x\right)-10x\leq 15+6$$

Add 15 and 6 to get 21.

$$5\left(-x\right)-10x\leq 21$$

Multiply 5 and -1 to get -5.

$$-5x-10x\leq 21$$

Combine -5x and -10x to get -15x.

$$-15x\leq 21$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x\geq \frac{21}{-15}$$

Reduce the fraction \frac{21}{-15} to lowest terms by extracting and canceling out 3.

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