Solve x-2/3+x+4/2geqx/4

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

Solve for x

$$x\geq -\frac{16}{7}$$

Solution Steps

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

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

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

$$4x-8+6\left(x+4\right)\geq 3x$$

Use the distributive property to multiply 6 by x+4.

$$4x-8+6x+24\geq 3x$$

Combine 4x and 6x to get 10x.

$$10x-8+24\geq 3x$$

Add -8 and 24 to get 16.

$$10x+16\geq 3x$$

Subtract 3x from both sides.

$$10x+16-3x\geq 0$$

Combine 10x and -3x to get 7x.

$$7x+16\geq 0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$7x\geq -16$$

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

$$x\geq -\frac{16}{7}$$