Solve 2/7(3-4x)+8>18

$$\frac { 2 } { 7 } ( 3 - 4 x ) + 8 > 18$$

Solve for x

$$x<-8$$

Solution Steps

Use the distributive property to multiply \frac{2}{7} by 3-4x.

$$\frac{2}{7}\times 3+\frac{2}{7}\left(-4\right)x+8>18$$

Express \frac{2}{7}\times 3 as a single fraction.

$$\frac{2\times 3}{7}+\frac{2}{7}\left(-4\right)x+8>18$$

Multiply 2 and 3 to get 6.

$$\frac{6}{7}+\frac{2}{7}\left(-4\right)x+8>18$$

Express \frac{2}{7}\left(-4\right) as a single fraction.

$$\frac{6}{7}+\frac{2\left(-4\right)}{7}x+8>18$$

Multiply 2 and -4 to get -8.

$$\frac{6}{7}+\frac{-8}{7}x+8>18$$

Fraction \frac{-8}{7} can be rewritten as -\frac{8}{7} by extracting the negative sign.

$$\frac{6}{7}-\frac{8}{7}x+8>18$$

Convert 8 to fraction \frac{56}{7}.

$$\frac{6}{7}-\frac{8}{7}x+\frac{56}{7}>18$$

Since \frac{6}{7} and \frac{56}{7} have the same denominator, add them by adding their numerators.

$$\frac{6+56}{7}-\frac{8}{7}x>18$$

Add 6 and 56 to get 62.

$$\frac{62}{7}-\frac{8}{7}x>18$$

Subtract \frac{62}{7} from both sides.

$$-\frac{8}{7}x>18-\frac{62}{7}$$

Convert 18 to fraction \frac{126}{7}.

$$-\frac{8}{7}x>\frac{126}{7}-\frac{62}{7}$$

Since \frac{126}{7} and \frac{62}{7} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{7}x>\frac{126-62}{7}$$

Subtract 62 from 126 to get 64.

$$-\frac{8}{7}x>\frac{64}{7}$$

Multiply both sides by -\frac{7}{8}, the reciprocal of -\frac{8}{7}. Since -\frac{8}{7} is negative, the inequality direction is changed.

$$x<\frac{64}{7}\left(-\frac{7}{8}\right)$$

Multiply \frac{64}{7} times -\frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{64\left(-7\right)}{7\times 8}$$

Do the multiplications in the fraction \frac{64\left(-7\right)}{7\times 8}.

$$x<\frac{-448}{56}$$

Divide -448 by 56 to get -8.

$$x<-8$$