Solve x-2/3+x+1/4geq5/2

$$\frac{ x-2 }{ 3 } + \frac{ x+1 }{ 4 } \geq \frac{ 5 }{ 2 }$$

Solve for x

$$x\geq 5$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4,2. Since 12 is positive, the inequality direction remains the same.

$$4\left(x-2\right)+3\left(x+1\right)\geq 30$$

Use the distributive property to multiply 4 by x-2.

$$4x-8+3\left(x+1\right)\geq 30$$

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

$$4x-8+3x+3\geq 30$$

Combine 4x and 3x to get 7x.

$$7x-8+3\geq 30$$

Add -8 and 3 to get -5.

$$7x-5\geq 30$$

Add 5 to both sides.

$$7x\geq 30+5$$

Add 30 and 5 to get 35.

$$7x\geq 35$$

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

$$x\geq \frac{35}{7}$$

Divide 35 by 7 to get 5.

$$x\geq 5$$