Solve 5x-1/8+2xgeqx-x+1/8

$$\frac { 5 x - 1 } { 8 } + 2 x \geq x - \frac { x + 1 } { 8 }$$

Solve for x

$$x\geq 0$$

Solution Steps

Multiply both sides of the equation by 8. Since 8 is positive, the inequality direction remains the same.

$$5x-1+16x\geq 8x-\left(x+1\right)$$

Combine 5x and 16x to get 21x.

$$21x-1\geq 8x-\left(x+1\right)$$

To find the opposite of x+1, find the opposite of each term.

$$21x-1\geq 8x-x-1$$

Combine 8x and -x to get 7x.

$$21x-1\geq 7x-1$$

Subtract 7x from both sides.

$$21x-1-7x\geq -1$$

Combine 21x and -7x to get 14x.

$$14x-1\geq -1$$

Add 1 to both sides.

$$14x\geq -1+1$$

Add -1 and 1 to get 0.

$$14x\geq 0$$

Product of two numbers is ≥0 if both are ≥0 or both are ≤0. Since 14\geq 0, x must be ≥0.

$$x\geq 0$$