Solve 2(x+1)-(7x+5/7-2)<0

$$2 ( x + 1 ) - ( \frac { 7 x + 5 } { 7 } - 2 ) < 0$$

Solve for x

$$x<-\frac{23}{7}$$

Solution Steps

Multiply both sides of the equation by 7. Since 7 is positive, the inequality direction remains the same.

$$14\left(x+1\right)-7\left(\frac{7x+5}{7}-2\right)<0$$

Use the distributive property to multiply 14 by x+1.

$$14x+14-7\left(\frac{7x+5}{7}-2\right)<0$$

Divide each term of 7x+5 by 7 to get x+\frac{5}{7}.

$$14x+14-7\left(x+\frac{5}{7}-2\right)<0$$

Convert 2 to fraction \frac{14}{7}.

$$14x+14-7\left(x+\frac{5}{7}-\frac{14}{7}\right)<0$$

Since \frac{5}{7} and \frac{14}{7} have the same denominator, subtract them by subtracting their numerators.

$$14x+14-7\left(x+\frac{5-14}{7}\right)<0$$

Subtract 14 from 5 to get -9.

$$14x+14-7\left(x-\frac{9}{7}\right)<0$$

Use the distributive property to multiply -7 by x-\frac{9}{7}.

$$14x+14-7x-7\left(-\frac{9}{7}\right)<0$$

Multiply -7 times -\frac{9}{7}.

$$14x+14-7x+9<0$$

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

$$7x+14+9<0$$

Add 14 and 9 to get 23.

$$7x+23<0$$

Subtract 23 from both sides. Anything subtracted from zero gives its negation.

$$7x<-23$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x<-\frac{23}{7}$$