Solve 13x-14/4<5-x/3

$$\frac { 13 x - 14 } { 4 } < \frac { 5 - x } { 3 }$$

Solve for x

$$x<\frac{62}{43}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(13x-14\right)<4\left(5-x\right)$$

Use the distributive property to multiply 3 by 13x-14.

$$39x-42<4\left(5-x\right)$$

Use the distributive property to multiply 4 by 5-x.

$$39x-42<20-4x$$

Add 4x to both sides.

$$39x-42+4x<20$$

Combine 39x and 4x to get 43x.

$$43x-42<20$$

Add 42 to both sides.

$$43x<20+42$$

Add 20 and 42 to get 62.

$$43x<62$$

Divide both sides by 43. Since 43 is positive, the inequality direction remains the same.

$$x<\frac{62}{43}$$