Solve 2+x/3geq2x-1/2

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

Solve for x

$$x\leq \frac{7}{4}$$

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.

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

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

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

Use the distributive property to multiply 3 by 2x-1.

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

Subtract 6x from both sides.

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

Combine 2x and -6x to get -4x.

$$4-4x\geq -3$$

Subtract 4 from both sides.

$$-4x\geq -3-4$$

Subtract 4 from -3 to get -7.

$$-4x\geq -7$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x\leq \frac{-7}{-4}$$

Fraction \frac{-7}{-4} can be simplified to \frac{7}{4} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{7}{4}$$