Solve 3x-4/5-(2-1/3)3x-3/10leq-x+2

$$\frac { 3 x - 4 } { 5 } - ( 2 - \frac { 1 } { 3 } ) \frac { 3 x - 3 } { 10 } \leq - x + 2$$

Solve for x

$$x\leq \frac{23}{11}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,3,10. Since 30 is positive, the inequality direction remains the same.

$$6\left(3x-4\right)-3\left(2-\frac{1}{3}\right)\left(3x-3\right)\leq -30x+60$$

Use the distributive property to multiply 6 by 3x-4.

$$18x-24-3\left(2-\frac{1}{3}\right)\left(3x-3\right)\leq -30x+60$$

Convert 2 to fraction \frac{6}{3}.

$$18x-24-3\left(\frac{6}{3}-\frac{1}{3}\right)\left(3x-3\right)\leq -30x+60$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$18x-24-3\times \frac{6-1}{3}\left(3x-3\right)\leq -30x+60$$

Subtract 1 from 6 to get 5.

$$18x-24-3\times \frac{5}{3}\left(3x-3\right)\leq -30x+60$$

Cancel out 3 and 3.

$$18x-24-5\left(3x-3\right)\leq -30x+60$$

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

$$18x-24-15x+15\leq -30x+60$$

Combine 18x and -15x to get 3x.

$$3x-24+15\leq -30x+60$$

Add -24 and 15 to get -9.

$$3x-9\leq -30x+60$$

Add 30x to both sides.

$$3x-9+30x\leq 60$$

Combine 3x and 30x to get 33x.

$$33x-9\leq 60$$

Add 9 to both sides.

$$33x\leq 60+9$$

Add 60 and 9 to get 69.

$$33x\leq 69$$

Divide both sides by 33. Since 33 is positive, the inequality direction remains the same.

$$x\leq \frac{69}{33}$$

Reduce the fraction \frac{69}{33} to lowest terms by extracting and canceling out 3.

$$x\leq \frac{23}{11}$$