Solve 2^7(x+1)-5<3(x-1)+4

$$2 ^ { 7 } ( x + 1 ) - 5 < 3 ( x - 1 ) + 4$$

Solve for x

$$x<-\frac{122}{125}$$

Solution Steps

Calculate 2 to the power of 7 and get 128.

$$128\left(x+1\right)-5<3\left(x-1\right)+4$$

Use the distributive property to multiply 128 by x+1.

$$128x+128-5<3\left(x-1\right)+4$$

Subtract 5 from 128 to get 123.

$$128x+123<3\left(x-1\right)+4$$

Use the distributive property to multiply 3 by x-1.

$$128x+123<3x-3+4$$

Add -3 and 4 to get 1.

$$128x+123<3x+1$$

Subtract 3x from both sides.

$$128x+123-3x<1$$

Combine 128x and -3x to get 125x.

$$125x+123<1$$

Subtract 123 from both sides.

$$125x<1-123$$

Subtract 123 from 1 to get -122.

$$125x<-122$$

Divide both sides by 125. Since 125 is positive, the inequality direction remains the same.

$$x<-\frac{122}{125}$$