Solve x+34/-6>2x-42/-3

$$\frac { x + 34 } { - 6 } > \frac { 2 x - 42 } { - 3 }$$

Solve for x

$$x>\frac{118}{3}$$

Solution Steps

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

$$-\left(x+34\right)>-2\left(2x-42\right)$$

To find the opposite of x+34, find the opposite of each term.

$$-x-34>-2\left(2x-42\right)$$

Use the distributive property to multiply -2 by 2x-42.

$$-x-34>-4x+84$$

Add 4x to both sides.

$$-x-34+4x>84$$

Combine -x and 4x to get 3x.

$$3x-34>84$$

Add 34 to both sides.

$$3x>84+34$$

Add 84 and 34 to get 118.

$$3x>118$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x>\frac{118}{3}$$