Question

Solve for b: 3 b minus 1 space less than space fraction numerator negative 7 b minus 21 over denominator negative 4 end fraction The solution is _____

Answer 1

$3b-1<\frac{-7b-21}{-4}$

To solve b:

1. Multiply both sides of the inequaltity by -4 (as you multiply both sides by a negative number the inequality sing flip):

$\begin{gathered} -4(3b-1)>\frac{-7b-21}{-4}\cdot(-4) \\ \\ -12b+4>-7b-21 \end{gathered}$

2. Add 7b in both sides of the inequality;

$\begin{gathered} -12b+7b+4>-7b+7b-21 \\ -5b+4>-21 \end{gathered}$

3. Substract 4 in both sides of the inequality

$\begin{gathered} -5b+4-4>-21-4 \\ -5b>-25 \end{gathered}$

4. Divide both sides of the inequality into -5 (as you divide both sides into a negative number the inequality sing flip):

$\begin{gathered} \frac{-5}{-5}b<\frac{-25}{-5} \\ \\ b<5 \end{gathered}$Then, the solution is b < 5