Solve 4x-1/5-2(3x-5)/3leqx+2

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

Solve for x

$$x\geq \frac{17}{33}$$

Solution Steps

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

$$3\left(4x-1\right)-5\times 2\left(3x-5\right)\leq 15x+30$$

Use the distributive property to multiply 3 by 4x-1.

$$12x-3-5\times 2\left(3x-5\right)\leq 15x+30$$

Multiply -5 and 2 to get -10.

$$12x-3-10\left(3x-5\right)\leq 15x+30$$

Use the distributive property to multiply -10 by 3x-5.

$$12x-3-30x+50\leq 15x+30$$

Combine 12x and -30x to get -18x.

$$-18x-3+50\leq 15x+30$$

Add -3 and 50 to get 47.

$$-18x+47\leq 15x+30$$

Subtract 15x from both sides.

$$-18x+47-15x\leq 30$$

Combine -18x and -15x to get -33x.

$$-33x+47\leq 30$$

Subtract 47 from both sides.

$$-33x\leq 30-47$$

Subtract 47 from 30 to get -17.

$$-33x\leq -17$$

Divide both sides by -33. Since -33 is negative, the inequality direction is changed.

$$x\geq \frac{-17}{-33}$$

Fraction \frac{-17}{-33} can be simplified to \frac{17}{33} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{17}{33}$$