Solve 2x-5<1/3+3x/4+3x/3

$$2 x - 5 < \frac { 1 } { 3 } + \frac { 3 x } { 4 } + \frac { 3 x } { 3 }$$

Solve for x

$$x<\frac{64}{3}$$

Solution Steps

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

$$24x-60<4+3\times 3x+4\times 3x$$

Multiply 3 and 3 to get 9. Multiply 4 and 3 to get 12.

$$24x-60<4+9x+12x$$

Combine 9x and 12x to get 21x.

$$24x-60<4+21x$$

Subtract 21x from both sides.

$$24x-60-21x<4$$

Combine 24x and -21x to get 3x.

$$3x-60<4$$

Add 60 to both sides.

$$3x<4+60$$

Add 4 and 60 to get 64.

$$3x<64$$

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

$$x<\frac{64}{3}$$