Unit Review: Multi-step equations

Q.1Q.2Q.3Solve for the variable.

1. 1
   $m-5=51+9m$
2. 2
   $-x-14=7x-78$
3. 3
   $-w+1=5w-5$
4. 4
   $5+6m=-19-6m$
5. 5
   $3(n-2)=-8n+49$
6. 6
   $-9(w-3)=3(w-6)+57$
7. 7
   $-3(p-1)=-6p+24$
8. 8
   $8(n-1)=-76-9n$
9. 9
   $\frac{4}{5}k+7=\frac{1}{4}k+40$
10. 10
    $\frac{2}{5}m+10=\frac{4}{3}m-18$
11. 11
    $\frac{4}{3}m+10=\frac{3}{2}m+7$
12. 12
    $\frac{7}{6}p+9=\frac{1}{4}p+31$

Q.4Write one solution (and give it), no solution, or infinitely many solutions.

1. 13
   $-3(x+3)=-3x-9$
2. 14
   $-8m+64+16m=8m+73$
3. 15
   $6(y+8)=-4y-22$
4. 16
   $5(x+3)=5x+15$

Q.5Write an equation and solve it.

1. 17
   Ava has $\text{\$}36.00$ and saves $\text{\$}4.00$ a week. Ben has $\text{\$}22.00$ and saves $\text{\$}11.00$ a week. After how many weeks will they have the same amount?
2. 18
   Ava has $\text{\$}82.00$ and saves $\text{\$}5.00$ a week. Ben has $\text{\$}47.00$ and saves $\text{\$}12.00$ a week. After how many weeks will they have the same amount?
3. 19
   Ava has $\text{\$}84.00$ and saves $\text{\$}7.00$ a week. Ben has $\text{\$}57.00$ and saves $\text{\$}10.00$ a week. After how many weeks will they have the same amount?

Q.6Solve for the variable.

1. 20
   $-8(n+2)=-5n-43$
2. 21
   $6(y-6)=3y-15$
3. 22
   $6(k-9)=8(k-1)-48$
4. 23
   $-9(p+8)=-5p-64$

Q.1Q.2Q.3Solve for the variable.

1. 1$m=-7$
2. 2$x=8$
3. 3$w=1$
4. 4$m=-2$
5. 5$n=5$
6. 6$w=-1$
7. 7$p=7$
8. 8$n=-4$
9. 9$k=60$
10. 10$m=30$
11. 11$m=18$
12. 12$p=24$

Q.4One, None, or Infinitely Many Solutions

1. 13infinitely many solutions
2. 14no solution
3. 15one solution: $y=-7$
4. 16infinitely many solutions

Q.5Equation Word Problems: Variables on Both Sides

1. 172 weeks
2. 185 weeks
3. 199 weeks

Q.6Multi-Step Equations Review

1. 20$n=9$
2. 21$y=7$
3. 22$k=1$
4. 23$p=-2$