Solve 12/7(b-5)=8b+24

$$\frac { 12 } { 7 } ( b - 5 ) = 8 b + 24$$

Solve for b

$$b = -\frac{57}{11} = -5\frac{2}{11} \approx -5.181818182$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{12}{7} by b-5.

$$\frac{12}{7}b+\frac{12}{7}\left(-5\right)=8b+24$$

Express \frac{12}{7}\left(-5\right) as a single fraction.

$$\frac{12}{7}b+\frac{12\left(-5\right)}{7}=8b+24$$

Multiply 12 and -5 to get -60.

$$\frac{12}{7}b+\frac{-60}{7}=8b+24$$

Fraction \frac{-60}{7} can be rewritten as -\frac{60}{7} by extracting the negative sign.

$$\frac{12}{7}b-\frac{60}{7}=8b+24$$

Subtract 8b from both sides.

$$\frac{12}{7}b-\frac{60}{7}-8b=24$$

Combine \frac{12}{7}b and -8b to get -\frac{44}{7}b.

$$-\frac{44}{7}b-\frac{60}{7}=24$$

Add \frac{60}{7} to both sides.

$$-\frac{44}{7}b=24+\frac{60}{7}$$

Convert 24 to fraction \frac{168}{7}.

$$-\frac{44}{7}b=\frac{168}{7}+\frac{60}{7}$$

Since \frac{168}{7} and \frac{60}{7} have the same denominator, add them by adding their numerators.

$$-\frac{44}{7}b=\frac{168+60}{7}$$

Add 168 and 60 to get 228.

$$-\frac{44}{7}b=\frac{228}{7}$$

Multiply both sides by -\frac{7}{44}, the reciprocal of -\frac{44}{7}.

$$b=\frac{228}{7}\left(-\frac{7}{44}\right)$$

Multiply \frac{228}{7} times -\frac{7}{44} by multiplying numerator times numerator and denominator times denominator.

$$b=\frac{228\left(-7\right)}{7\times 44}$$

Do the multiplications in the fraction \frac{228\left(-7\right)}{7\times 44}.

$$b=\frac{-1596}{308}$$

Reduce the fraction \frac{-1596}{308} to lowest terms by extracting and canceling out 28.

$$b=-\frac{57}{11}$$