Solve 5x-(3x-2)/25--25(-2x/3)+5x/20leq-2x-frac{1/5}{10}-frac{3(5(5x-3)-3x)}{15}

$$\frac{ 5x-(3x-2) }{ 25 } - \frac{ -25(-2 \frac{ x }{ 3 } )+5x }{ 20 } \leq - \frac{ 2x- \frac{ 1 }{ 5 } }{ 10 } - \frac{ 3(5(5x-3)-3x) }{ 15 }$$

Solve for x

$$x\leq \frac{882}{1079}$$

Solution Steps

Multiply both sides of the equation by 300, the least common multiple of 25,20,10,15. Since 300 is positive, the inequality direction remains the same.

$$12\left(5x-\left(3x-2\right)\right)-15\left(-25\left(-2\right)\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

To find the opposite of 3x-2, find the opposite of each term.

$$12\left(5x-3x-\left(-2\right)\right)-15\left(-25\left(-2\right)\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

The opposite of -2 is 2.

$$12\left(5x-3x+2\right)-15\left(-25\left(-2\right)\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Combine 5x and -3x to get 2x.

$$12\left(2x+2\right)-15\left(-25\left(-2\right)\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Use the distributive property to multiply 12 by 2x+2.

$$24x+24-15\left(-25\left(-2\right)\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Multiply -25 and -2 to get 50.

$$24x+24-15\left(50\times \frac{x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Express 50\times \frac{x}{3} as a single fraction.

$$24x+24-15\left(\frac{50x}{3}+5x\right)\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Use the distributive property to multiply -15 by \frac{50x}{3}+5x.

$$24x+24-15\times \frac{50x}{3}-75x\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Cancel out 3, the greatest common factor in 15 and 3.

$$24x+24-5\times 50x-75x\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Multiply -5 and 50 to get -250.

$$24x+24-250x-75x\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Combine -250x and -75x to get -325x.

$$24x+24-325x\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Combine 24x and -325x to get -301x.

$$-301x+24\leq -30\left(2x-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Use the distributive property to multiply -30 by 2x-\frac{1}{5}.

$$-301x+24\leq -60x-30\left(-\frac{1}{5}\right)-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Express -30\left(-\frac{1}{5}\right) as a single fraction.

$$-301x+24\leq -60x+\frac{-30\left(-1\right)}{5}-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Multiply -30 and -1 to get 30.

$$-301x+24\leq -60x+\frac{30}{5}-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Divide 30 by 5 to get 6.

$$-301x+24\leq -60x+6-20\times 3\left(5\left(5x-3\right)-3x\right)$$

Multiply -20 and 3 to get -60.

$$-301x+24\leq -60x+6-60\left(5\left(5x-3\right)-3x\right)$$

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

$$-301x+24\leq -60x+6-60\left(25x-15-3x\right)$$

Combine 25x and -3x to get 22x.

$$-301x+24\leq -60x+6-60\left(22x-15\right)$$

Use the distributive property to multiply -60 by 22x-15.

$$-301x+24\leq -60x+6-1320x+900$$

Combine -60x and -1320x to get -1380x.

$$-301x+24\leq -1380x+6+900$$

Add 6 and 900 to get 906.

$$-301x+24\leq -1380x+906$$

Add 1380x to both sides.

$$-301x+24+1380x\leq 906$$

Combine -301x and 1380x to get 1079x.

$$1079x+24\leq 906$$

Subtract 24 from both sides.

$$1079x\leq 906-24$$

Subtract 24 from 906 to get 882.

$$1079x\leq 882$$

Divide both sides by 1079. Since 1079 is positive, the inequality direction remains the same.

$$x\leq \frac{882}{1079}$$