Solve 2(x-3)leq3(1-x)+1

$$2 ( x - 3 ) \leq 3 ( 1 - x ) + 1$$

Solve for x

$$x\leq 2$$

Solution Steps

Use the distributive property to multiply 2 by x-3.

$$2x-6\leq 3\left(1-x\right)+1$$

Use the distributive property to multiply 3 by 1-x.

$$2x-6\leq 3-3x+1$$

Add 3 and 1 to get 4.

$$2x-6\leq 4-3x$$

Add 3x to both sides.

$$2x-6+3x\leq 4$$

Combine 2x and 3x to get 5x.

$$5x-6\leq 4$$

Add 6 to both sides.

$$5x\leq 4+6$$

Add 4 and 6 to get 10.

$$5x\leq 10$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$x\leq \frac{10}{5}$$

Divide 10 by 5 to get 2.

$$x\leq 2$$