Suggested languages for you:

Americas

Europe

Q5

Expert-verifiedFound in: Page 41

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

Justify each step.

$\frac{2}{3}b=8-2b$

$2b=3\left(8-2b\right)$

$2b=24-6b$

$8b=24$

$b=3$

$\frac{2}{3}b=8-2b$ Given

$2b=3\left(8-2b\right)$ Multiplication property of equality

$2b=24-6b$ Distributive property

$8b=24$ Addition property of equality.

$b=3$ Division property of equality

If $p=q$ then, $rp=rq$.

Multiply each side of the $\frac{2}{3}b=8-2b$ by 3 and simplify.

$\begin{array}{c}3\times \frac{2}{3}b=3\left(8-2b\right)\\ 2b=3\left(8-2b\right)\end{array}$

Expand the right-hand side of the equation obtained in step 2 using the distributive property.

$\begin{array}{c}2b=3\times 8-3\times \left(2b\right)\\ =24-6b\end{array}$

If $p=q$ and $r=s$, then $p+r=q+s$.

Add $6b$ on each side of $2b=24-6b$ and simplify.

$2b+6b=24-6b+6b$

$8b=24$

If $p=q$ and $r\ne 0$, then $\frac{p}{r}=\frac{q}{r}$.

Divide each side of the equation obtained in steps 5 by 8 to find the value of *b*.

$\begin{array}{c}\frac{8b}{8}=\frac{24}{8}\\ b=3\end{array}$

Therefore, the value of *b* is 3.

94% of StudySmarter users get better grades.

Sign up for free