Solve 7-x/10-3x-1/5+x-4/3<7

$$\frac { 7 - x } { 10 } - \frac { 3 x - 1 } { 5 } + \frac { x - 4 } { 3 } < 7$$

Solve for x

$$x>-\frac{223}{11}$$

Solution Steps

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

$$3\left(7-x\right)-6\left(3x-1\right)+10\left(x-4\right)<210$$

Use the distributive property to multiply 3 by 7-x.

$$21-3x-6\left(3x-1\right)+10\left(x-4\right)<210$$

Use the distributive property to multiply -6 by 3x-1.

$$21-3x-18x+6+10\left(x-4\right)<210$$

Combine -3x and -18x to get -21x.

$$21-21x+6+10\left(x-4\right)<210$$

Add 21 and 6 to get 27.

$$27-21x+10\left(x-4\right)<210$$

Use the distributive property to multiply 10 by x-4.

$$27-21x+10x-40<210$$

Combine -21x and 10x to get -11x.

$$27-11x-40<210$$

Subtract 40 from 27 to get -13.

$$-13-11x<210$$

Add 13 to both sides.

$$-11x<210+13$$

Add 210 and 13 to get 223.

$$-11x<223$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x>-\frac{223}{11}$$