Solve 2/5(x-1)+8<10

$$\frac { 2 } { 5 } ( x - 1 ) + 8 < 10$$

Solve for x

$$x<6$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by x-1.

$$\frac{2}{5}x+\frac{2}{5}\left(-1\right)+8<10$$

Multiply \frac{2}{5} and -1 to get -\frac{2}{5}.

$$\frac{2}{5}x-\frac{2}{5}+8<10$$

Convert 8 to fraction \frac{40}{5}.

$$\frac{2}{5}x-\frac{2}{5}+\frac{40}{5}<10$$

Since -\frac{2}{5} and \frac{40}{5} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}x+\frac{-2+40}{5}<10$$

Add -2 and 40 to get 38.

$$\frac{2}{5}x+\frac{38}{5}<10$$

Subtract \frac{38}{5} from both sides.

$$\frac{2}{5}x<10-\frac{38}{5}$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{2}{5}x<\frac{50}{5}-\frac{38}{5}$$

Since \frac{50}{5} and \frac{38}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}x<\frac{50-38}{5}$$

Subtract 38 from 50 to get 12.

$$\frac{2}{5}x<\frac{12}{5}$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}. Since \frac{2}{5} is positive, the inequality direction remains the same.

$$x<\frac{12}{5}\times \frac{5}{2}$$

Multiply \frac{12}{5} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{12\times 5}{5\times 2}$$

Cancel out 5 in both numerator and denominator.

$$x<\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x<6$$