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

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

Solve for x

$$x<\frac{5}{3}$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$4-3x-3<3\left(7-5x\right)$$

Subtract 3 from 4 to get 1.

$$1-3x<3\left(7-5x\right)$$

Use the distributive property to multiply 3 by 7-5x.

$$1-3x<21-15x$$

Add 15x to both sides.

$$1-3x+15x<21$$

Combine -3x and 15x to get 12x.

$$1+12x<21$$

Subtract 1 from both sides.

$$12x<21-1$$

Subtract 1 from 21 to get 20.

$$12x<20$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$x<\frac{20}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$x<\frac{5}{3}$$