Solve 2x+1/3-1-x/2leq1

$$\frac { 2 x + 1 } { 3 } - \frac { 1 - x } { 2 } \leq 1$$

Solve for x

$$x\leq 1$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 2 by 2x+1.

$$4x+2-3\left(1-x\right)\leq 6$$

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

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

Subtract 3 from 2 to get -1.

$$4x-1+3x\leq 6$$

Combine 4x and 3x to get 7x.

$$7x-1\leq 6$$

Add 1 to both sides.

$$7x\leq 6+1$$

Add 6 and 1 to get 7.

$$7x\leq 7$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x\leq \frac{7}{7}$$

Divide 7 by 7 to get 1.

$$x\leq 1$$