Solve -6x-2/3leq3x/2+1/2

$$\frac { - 6 x - 2 } { 3 } \leq \frac { 3 x } { 2 } + \frac { 1 } { 2 }$$

Solve for x

$$x\geq -\frac{1}{3}$$

Solution Steps

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

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

Use the distributive property to multiply 2 by -6x-2.

$$-12x-4\leq 3\times 3x+3$$

Multiply 3 and 3 to get 9.

$$-12x-4\leq 9x+3$$

Subtract 9x from both sides.

$$-12x-4-9x\leq 3$$

Combine -12x and -9x to get -21x.

$$-21x-4\leq 3$$

Add 4 to both sides.

$$-21x\leq 3+4$$

Add 3 and 4 to get 7.

$$-21x\leq 7$$

Divide both sides by -21. Since -21 is negative, the inequality direction is changed.

$$x\geq \frac{7}{-21}$$

Reduce the fraction \frac{7}{-21} to lowest terms by extracting and canceling out 7.

$$x\geq -\frac{1}{3}$$