Solve 2x-5<1/3+3x/4+1-x/3+12

$$2 x - 5 < \frac { 1 } { 3 } + \frac { 3 x } { 4 } + \frac { 1 - x } { 3 } + 12$$

Solve for x

$$x<\frac{212}{19}$$

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.

$$24x-60<4+3\times 3x+4\left(1-x\right)+144$$

Multiply 3 and 3 to get 9.

$$24x-60<4+9x+4\left(1-x\right)+144$$

Use the distributive property to multiply 4 by 1-x.

$$24x-60<4+9x+4-4x+144$$

Add 4 and 4 to get 8.

$$24x-60<8+9x-4x+144$$

Combine 9x and -4x to get 5x.

$$24x-60<8+5x+144$$

Add 8 and 144 to get 152.

$$24x-60<152+5x$$

Subtract 5x from both sides.

$$24x-60-5x<152$$

Combine 24x and -5x to get 19x.

$$19x-60<152$$

Add 60 to both sides.

$$19x<152+60$$

Add 152 and 60 to get 212.

$$19x<212$$

Divide both sides by 19. Since 19 is positive, the inequality direction remains the same.

$$x<\frac{212}{19}$$