Solve 1/3(11x-12)leq12-1/3x

$$\frac{ 1 }{ 3 } (11x-12) \leq 12- \frac{ 1 }{ 3 } x$$

Solve for x

$$x\leq 4$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 11x-12.

$$\frac{1}{3}\times 11x+\frac{1}{3}\left(-12\right)\leq 12-\frac{1}{3}x$$

Multiply \frac{1}{3} and 11 to get \frac{11}{3}.

$$\frac{11}{3}x+\frac{1}{3}\left(-12\right)\leq 12-\frac{1}{3}x$$

Multiply \frac{1}{3} and -12 to get \frac{-12}{3}.

$$\frac{11}{3}x+\frac{-12}{3}\leq 12-\frac{1}{3}x$$

Divide -12 by 3 to get -4.

$$\frac{11}{3}x-4\leq 12-\frac{1}{3}x$$

Add \frac{1}{3}x to both sides.

$$\frac{11}{3}x-4+\frac{1}{3}x\leq 12$$

Combine \frac{11}{3}x and \frac{1}{3}x to get 4x.

$$4x-4\leq 12$$

Add 4 to both sides.

$$4x\leq 12+4$$

Add 12 and 4 to get 16.

$$4x\leq 16$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\leq \frac{16}{4}$$

Divide 16 by 4 to get 4.

$$x\leq 4$$