2.4 Use a general strategy to solve linear equations  (Page 3/6)

$15\left(y-9\right)=\mathrm{-60}$

$21\left(y-5\right)=\mathrm{-42}$

$\mathrm{-9}\left(2n+1\right)=36$

$\mathrm{-16}\left(3n+4\right)=32$

$8\left(22+11r\right)=0$

$5\left(8+6p\right)=0$

$\text{−}\left(w-12\right)=30$

$\text{−}\left(t-19\right)=28$

$9\left(6a+8\right)+9=81$

$8\left(9b-4\right)-12=100$

$32+3(z+4)=41$

$21+2(m-4)=25$

$51+5(4-q)=56$

$\mathrm{-6}+6(5-k)=15$

$2(9s-6)-62=16$

$8(6t-5)-35=\mathrm{-27}$

$3(10-2x)+54=0$

$\mathrm{-2}(11-7x)+54=4$

$\frac{2}{3}\left(9c-3\right)=22$

$\frac{3}{5}\left(10x-5\right)=27$

$\frac{1}{5}(15c+10)=c+7$

$\frac{1}{4}(20d+12)=d+7$

$18-(9r+7)=\mathrm{-16}$

$15-(3r+8)=28$

$5-(n-1)=19$

$\mathrm{-3}-(m-1)=13$

$11-4(y-8)=43$

$18-2(y-3)=32$

$24-8(3v+6)=0$

$35-5(2w+8)=\mathrm{-10}$

$4(a-12)=3\left(a+5\right)$

$\mathrm{-2}(a-6)=4\left(a-3\right)$

$2(5-u)=\mathrm{-3}\left(2u+6\right)$

$5(8-r)=\mathrm{-2}\left(2r-16\right)$

$3(4n-1)-2=8n+3$

$9(2m-3)-8=4m+7$

$12+2(5-3y)=\mathrm{-9}\left(y-1\right)-2$

$\mathrm{-15}+4(2-5y)=\mathrm{-7}\left(y-4\right)+4$

$8\left(x-4\right)-7x=14$

$5\left(x-4\right)-4x=14$

$5+6(3s-5)=\mathrm{-3}+2\left(8s-1\right)$

$\mathrm{-12}+8(x-5)=\mathrm{-4}+3\left(5x-2\right)$

$4\left(u-1\right)-8=6\left(3u-2\right)-7$

$7\left(2n-5\right)=8\left(4n-1\right)-9$

$4\left(p-4\right)-\left(p+7\right)=5\left(p-3\right)$

$3\left(a-2\right)-\left(a+6\right)=4\left(a-1\right)$

$\text{−}(9y+5)-(3y-7)$
$=16-(4y-2)$

$\text{−}\left(7m+4\right)-\left(2m-5\right)$
$=14-\left(5m-3\right)$

$4\left[5-8\left(4c-3\right)\right]$
$=12\left(1-13c\right)-8$

$5\left[9-2\left(6d-1\right)\right]$
$=11\left(4-10d\right)-139$

$3\left[\mathrm{-9}+8\left(4h-3\right)\right]$
$=2\left(5-12h\right)-19$

$3\left[\mathrm{-14}+2\left(15k-6\right)\right]$
$=8\left(3-5k\right)-24$

$5\left[2\left(m+4\right)+8\left(m-7\right)\right]$
$=2\left[3\left(5+m\right)-\left(21-3m\right)\right]$

$10\left[5\left(n+1\right)+4\left(n-1\right)\right]$
$=11[7\left(5+n\right)-\left(25-3n\right)]$

$5\left(1.2u-4.8\right)=\mathrm{-12}$

$4\left(2.5v-0.6\right)=7.6$

$0.25(q-6)=0.1\left(q+18\right)$

$0.2(p-6)=0.4\left(p+14\right)$

$0.2\left(30n+50\right)=28$

$0.5\left(16m+34\right)=\mathrm{-15}$

Fencing Micah has 44 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, L , by solving the equation $2L+2(L-2.5)=44$ .

Coins Rhonda has $1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, n , by solving the equation $0.05n+0.10(2n-1)=1.90$ .

Using your own words, list the steps in the general strategy for solving linear equations.

Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.

What is the first step you take when solving the equation $3-7(y-4)=38$ ? Why is this your first step?

Solve the equation $\frac{1}{4}\left(8x+20\right)=3x-4$ explaining all the steps of your solution as in the examples in this section.