Solve x+1/2+3(2x-1)/2geqx+3/4

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

Solve for x

$$x\geq \frac{7}{13}$$

Solution Steps

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

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

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

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

Multiply 2 and 3 to get 6.

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

Use the distributive property to multiply 6 by 2x-1.

$$2x+2+12x-6\geq x+3$$

Combine 2x and 12x to get 14x.

$$14x+2-6\geq x+3$$

Subtract 6 from 2 to get -4.

$$14x-4\geq x+3$$

Subtract x from both sides.

$$14x-4-x\geq 3$$

Combine 14x and -x to get 13x.

$$13x-4\geq 3$$

Add 4 to both sides.

$$13x\geq 3+4$$

Add 3 and 4 to get 7.

$$13x\geq 7$$

Divide both sides by 13. Since 13 is positive, the inequality direction remains the same.

$$x\geq \frac{7}{13}$$