Solve 7x+1/5-1geqx-1/2

$$\frac { 7 x + 1 } { 5 } - 1 \geq \frac { x - 1 } { 2 }$$

Solve for x

$$x\geq \frac{1}{3}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(7x+1\right)-10\geq 5\left(x-1\right)$$

Use the distributive property to multiply 2 by 7x+1.

$$14x+2-10\geq 5\left(x-1\right)$$

Subtract 10 from 2 to get -8.

$$14x-8\geq 5\left(x-1\right)$$

Use the distributive property to multiply 5 by x-1.

$$14x-8\geq 5x-5$$

Subtract 5x from both sides.

$$14x-8-5x\geq -5$$

Combine 14x and -5x to get 9x.

$$9x-8\geq -5$$

Add 8 to both sides.

$$9x\geq -5+8$$

Add -5 and 8 to get 3.

$$9x\geq 3$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x\geq \frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$x\geq \frac{1}{3}$$