Solve x-7x+1/5geq1-1-x/10

$$x - \frac { 7 x + 1 } { 5 } \geq 1 - \frac { 1 - x } { 10 }$$

Solve for x

$$x\leq -\frac{11}{5}$$

Solution Steps

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

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

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

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

Combine 10x and -14x to get -4x.

$$-4x-2\geq 10-\left(1-x\right)$$

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

$$-4x-2\geq 10-1-\left(-x\right)$$

The opposite of -x is x.

$$-4x-2\geq 10-1+x$$

Subtract 1 from 10 to get 9.

$$-4x-2\geq 9+x$$

Subtract x from both sides.

$$-4x-2-x\geq 9$$

Combine -4x and -x to get -5x.

$$-5x-2\geq 9$$

Add 2 to both sides.

$$-5x\geq 9+2$$

Add 9 and 2 to get 11.

$$-5x\geq 11$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$x\leq -\frac{11}{5}$$