Solve x-(5x-1)leq7-5x/10+11x

$$x - ( 5 x - 1 ) \leq \frac { 7 - 5 x } { 10 } + 11 x$$

Solve for x

$$x\geq \frac{3}{145}$$

Solution Steps

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

$$10x-10\left(5x-1\right)\leq 7-5x+110x$$

Use the distributive property to multiply -10 by 5x-1.

$$10x-50x+10\leq 7-5x+110x$$

Combine 10x and -50x to get -40x.

$$-40x+10\leq 7-5x+110x$$

Combine -5x and 110x to get 105x.

$$-40x+10\leq 7+105x$$

Subtract 105x from both sides.

$$-40x+10-105x\leq 7$$

Combine -40x and -105x to get -145x.

$$-145x+10\leq 7$$

Subtract 10 from both sides.

$$-145x\leq 7-10$$

Subtract 10 from 7 to get -3.

$$-145x\leq -3$$

Divide both sides by -145. Since -145 is negative, the inequality direction is changed.

$$x\geq \frac{-3}{-145}$$

Fraction \frac{-3}{-145} can be simplified to \frac{3}{145} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{3}{145}$$