다단계 방정식 단원 종합

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

1. 1
   $-8n+22=12-6n$
2. 2
   $20+4n=3n+21$
3. 3
   $19-9p=-2p+33$
4. 4
   $22-8y=6y+50$
5. 5
   $5(p+7)=3p+53$
6. 6
   $-6(n-8)=5n+59$
7. 7
   $4(k-4)=-2(k+1)+10$
8. 8
   $-6(w+6)=-24-4w$
9. 9
   $\frac{3}{4}w+7=\frac{1}{6}w+14$
10. 10
    $\frac{2}{5}y+11=\frac{1}{6}y+18$
11. 11
    $\frac{3}{5}x+2=\frac{4}{3}x-9$
12. 12
    $\frac{11}{6}w+3=\frac{2}{3}w+10$

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

1. 13
   $-4k+2+6k=2k+2$
2. 14
   $-9(n-9)=-9n+81$
3. 15
   $-7(w-4)=-7w+30$
4. 16
   $-7(m+9)=-7m-62$

Q.5Write an equation and solve it.

1. 17
   Candle A is $22$ cm tall and burns $4$ cm per hour. Candle B is $10$ cm tall and burns $1$ cm per hour. After how many hours will they be the same height?
2. 18
   Candle A is $31$ cm tall and burns $5$ cm per hour. Candle B is $19$ cm tall and burns $1$ cm per hour. After how many hours will they be the same height?
3. 19
   Ava has $\text{\$}87.00$ and saves $\text{\$}5.00$ a week. Ben has $\text{\$}73.00$ and saves $\text{\$}12.00$ a week. After how many weeks will they have the same amount?

Q.6Solve for the variable.

1. 20
   $3(m+1)=-5(m+4)+15$
2. 21
   $-2(y-5)=-11-5y$
3. 22
   $9(x-7)=-8x-29$
4. 23
   $3(w+4)=18-3w$

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

1. 1$n=5$
2. 2$n=1$
3. 3$p=-2$
4. 4$y=-2$
5. 5$p=9$
6. 6$n=-1$
7. 7$k=4$
8. 8$w=-6$
9. 9$w=12$
10. 10$y=30$
11. 11$x=15$
12. 12$w=6$

Q.4One, None, or Infinitely Many Solutions

1. 13infinitely many solutions
2. 14infinitely many solutions
3. 15no solution
4. 16no solution

Q.5Equation Word Problems: Variables on Both Sides

1. 174 hours
2. 183 hours
3. 192 weeks

Q.6Multi-Step Equations Review

1. 20$m=-1$
2. 21$y=-7$
3. 22$x=2$
4. 23$w=1$