Solve 1+x/2geq2x-5/-3

$$\frac { 1 + x } { 2 } \geq \frac { 2 x - 5 } { - 3 }$$

Solve for x

$$x\geq 1$$

Solution Steps

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

$$3\left(1+x\right)\geq -2\left(2x-5\right)$$

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

$$3+3x\geq -2\left(2x-5\right)$$

Use the distributive property to multiply -2 by 2x-5.

$$3+3x\geq -4x+10$$

Add 4x to both sides.

$$3+3x+4x\geq 10$$

Combine 3x and 4x to get 7x.

$$3+7x\geq 10$$

Subtract 3 from both sides.

$$7x\geq 10-3$$

Subtract 3 from 10 to get 7.

$$7x\geq 7$$

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

$$x\geq \frac{7}{7}$$

Divide 7 by 7 to get 1.

$$x\geq 1$$