Solve 1/2(3x-1)leq5-2x-3/3quad(8)

$$\frac { 1 } { 2 } ( 3 x - 1 ) \leq 5 - \frac { 2 x - 3 } { 3 } \quad ( 8 )$$

Solve for x

$$x\leq \frac{81}{41}$$

Solution Steps

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

$$3\left(3x-1\right)\leq 30-2\left(2x-3\right)\times 8$$

Use the distributive property to multiply 3 by 3x-1.

$$9x-3\leq 30-2\left(2x-3\right)\times 8$$

Multiply 2 and 8 to get 16.

$$9x-3\leq 30-16\left(2x-3\right)$$

Use the distributive property to multiply -16 by 2x-3.

$$9x-3\leq 30-32x+48$$

Add 30 and 48 to get 78.

$$9x-3\leq 78-32x$$

Add 32x to both sides.

$$9x-3+32x\leq 78$$

Combine 9x and 32x to get 41x.

$$41x-3\leq 78$$

Add 3 to both sides.

$$41x\leq 78+3$$

Add 78 and 3 to get 81.

$$41x\leq 81$$

Divide both sides by 41. Since 41 is positive, the inequality direction remains the same.

$$x\leq \frac{81}{41}$$