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

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

Solve for x

$$x\geq 3$$

Solution Steps

Multiply both sides of the equation by 35, the least common multiple of 7,5. Since 35 is positive, the inequality direction remains the same.

$$5\left(5x-1\right)\geq 35x-7\left(2x-1\right)$$

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

$$25x-5\geq 35x-7\left(2x-1\right)$$

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

$$25x-5\geq 35x-14x+7$$

Combine 35x and -14x to get 21x.

$$25x-5\geq 21x+7$$

Subtract 21x from both sides.

$$25x-5-21x\geq 7$$

Combine 25x and -21x to get 4x.

$$4x-5\geq 7$$

Add 5 to both sides.

$$4x\geq 7+5$$

Add 7 and 5 to get 12.

$$4x\geq 12$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x\geq \frac{12}{4}$$

Divide 12 by 4 to get 3.

$$x\geq 3$$