Solve x+5/7+10-3x/5>2x+7/3-148/21

$$\frac { x + 5 } { 7 } + \frac { 10 - 3 x } { 5 } > \frac { 2 x + 7 } { 3 } - \frac { 148 } { 21 }$$

Solve for x

$$x<\frac{390}{59}$$

Solution Steps

Multiply both sides of the equation by 105, the least common multiple of 7,5,3,21. Since 105 is positive, the inequality direction remains the same.

$$15\left(x+5\right)+21\left(10-3x\right)>35\left(2x+7\right)-740$$

Use the distributive property to multiply 15 by x+5.

$$15x+75+21\left(10-3x\right)>35\left(2x+7\right)-740$$

Use the distributive property to multiply 21 by 10-3x.

$$15x+75+210-63x>35\left(2x+7\right)-740$$

Add 75 and 210 to get 285.

$$15x+285-63x>35\left(2x+7\right)-740$$

Combine 15x and -63x to get -48x.

$$-48x+285>35\left(2x+7\right)-740$$

Use the distributive property to multiply 35 by 2x+7.

$$-48x+285>70x+245-740$$

Subtract 740 from 245 to get -495.

$$-48x+285>70x-495$$

Subtract 70x from both sides.

$$-48x+285-70x>-495$$

Combine -48x and -70x to get -118x.

$$-118x+285>-495$$

Subtract 285 from both sides.

$$-118x>-495-285$$

Subtract 285 from -495 to get -780.

$$-118x>-780$$

Divide both sides by -118. Since -118 is negative, the inequality direction is changed.

$$x<\frac{-780}{-118}$$

Reduce the fraction \frac{-780}{-118} to lowest terms by extracting and canceling out -2.

$$x<\frac{390}{59}$$