3.5 Solve equations using integers; the division property of  (Page 4/5)

$5x=45$

$4p=64$

$\mathrm{-7}c=56$

$\mathrm{-9}x=54$

$\mathrm{-14}p=\mathrm{-42}$

$\mathrm{-8}m=\mathrm{-40}$

$\mathrm{-120}=10q$

$\mathrm{-75}=15y$

$24x=480$

$18n=540$

$\mathrm{-3}z=0$

$4u=0$

$\text{Four more than}n\text{is equal to 1.}$

$\text{Nine more than}m\text{is equal to 5.}$

$\text{The sum of eight and}p\text{is}\mathrm{-3}.$

$\text{The sum of two and}q\text{is}\mathrm{-7}.$

$\text{The difference of}b\text{and}\text{5 is}\mathrm{-2}.$

$\text{The product of}f\text{and −15 is 75.}$

$\text{The product of}g\text{and −18 is 36.}$

$\text{−6 plus}c\text{is equal to 4.}$

$\text{−2 plus}d\text{is equal to 1.}$

$\text{Nine less than}n\text{is −4.}$

$\text{Thirteen less than}n\text{is}\mathrm{-10}.$

1. ⓐ $y+6=12$
2. ⓑ $6y=12$

$a-4=16$

$b-1=11$

$\mathrm{-8}m=\mathrm{-56}$

$\mathrm{-6}n=\mathrm{-48}$

$\mathrm{-39}=u+13$

$\mathrm{-100}=v+25$

$11r=\mathrm{-99}$

$15s=\mathrm{-300}$

$100=20d$

$250=25n$

$\mathrm{-49}=x-7$

$64=y-4$

Cookie packaging A package of $\text{51 cookies}$ has $3$ equal rows of cookies. Find the number of cookies in each row, $c,$ by solving the equation $3c=51.$

Kindergarten class Connie’s kindergarten class has $\text{24 children.}$ She wants them to get into $4$ equal groups. Find the number of children in each group, $g,$ by solving the equation $4g=24.$

Is modeling the Division Property of Equality with envelopes and counters helpful to understanding how to solve the equation $3x=15?$ Explain why or why not.

Suppose you are using envelopes and counters to model solving the equations $x+4=12$ and $4x=12.$ Explain how you would solve each equation.

Frida started to solve the equation $\mathrm{-3}x=36$ by adding $3$ to both sides. Explain why Frida’s method will not solve the equation.

Raoul started to solve the equation $4y=40$ by subtracting $4$ from both sides. Explain why Raoul’s method will not solve the equation.

$5$

$\mathrm{-5}$

$\mathrm{-3}$

$3$

$\mathrm{-8}$

$\mathrm{-7}$

$4\text{\_\_}8$

$\mathrm{-6}\text{\_\_}3$

$\mathrm{-5}\text{\_\_}\mathrm{-10}$

$\mathrm{-9}\text{\_\_}\mathrm{-4}$

$2\text{\_\_}\mathrm{-7}$

$\mathrm{-3}\text{\_\_}1$

$6$

$\mathrm{-2}$

$\mathrm{-4}$

$3$

1. ⓐ $-(8)$
2. ⓑ $-(\mathrm{-8})$

1. ⓐ $-(9)$
2. ⓑ $-(\mathrm{-9})$

$-x,\text{when}$

1. ⓐ $x=32$
2. ⓑ $x=\mathrm{-32}$

$-n,\text{when}$

1. ⓐ $n=20$
2. ⓐ $n=\mathrm{-20}$