Question

kuta software - infinite algebra 1
name
multi - step equations
date
p
solve each equation.

1. $-20 = -4x - 6x$
2. $6 = 1 - 2n + 5$
3. $8x - 2 = -9 + 7x$
4. $a + 5 = -5a + 5$
5. $4m - 4 = 4m$
6. $p - 1 = 5p + 3p - 8$
7. $5p - 14 = 8p + 4$
8. $p - 4 = -9 + p$
9. $-8 = -(x + 4)$
10. $12 = -4(-6x - 3)$
11. $14 = -(p - 8)$
12. $-(7 - 4x) = 9$
13. $-18 - 6k = 6(1 + 3k)$
14. $5n + 34 = -2(1 - 7n)$
15. $2(4x - 3) - 8 = 4 + 2x$
16. $3n - 5 = -8(6 + 5n)$
17. $-(1 + 7x) - 6(-7 - x) = 36$
18. $-3(4x + 3) + 4(6x + 1) = 43$
19. $24a - 22 = -4(1 - 6a)$
20. $-5(1 - 5x) + 5(-8x - 2) = -4x - 8x$

Explanation:

1) Step1: Combine like terms

$-20=-10x$
Step2: Solve for $x$
$x=2$

2) Step1: Combine constants

$6=6-2n$
Step2: Solve for $n$
$n=0$

3) Step1: Move $7x$ left

$x-2=-9$
Step2: Solve for $x$
$x=-7$

4) Step1: Move $-5a$ right

$6a+5=5$
Step2: Solve for $a$
$a=0$

5) Step1: Subtract $4m$

$-4=0$
Step2: Conclusion
No solution

6) Step1: Combine like terms

$p-1=8p-8$
Step2: Solve for $p$
$p=1$

7) Step1: Move $5p$ right

$-14=3p+4$
Step2: Solve for $p$
$p=-6$

8) Step1: Subtract $p$

$-4=-9$
Step2: Conclusion
No solution

9) Step1: Distribute negative

$-8=-x-4$
Step2: Solve for $x$
$x=4$

10) Step1: Distribute $-4$

$12=24x+12$
Step2: Solve for $x$
$x=0$

11) Step1: Distribute negative

$14=-p+8$
Step2: Solve for $p$
$p=-6$

12) Step1: Distribute negative

$-7+4x=9$
Step2: Solve for $x$
$x=4$

13) Step1: Distribute $6$

$-18-6k=6+18k$
Step2: Solve for $k$
$k=-1$

14) Step1: Distribute $-2$

$5n+34=-2+14n$
Step2: Solve for $n$
$n=4$

15) Step1: Distribute $2$

$8x-6-8=4+2x$
Step2: Solve for $x$
$x=9$

16) Step1: Distribute $-8$

$3n-5=-48-40n$
Step2: Solve for $n$
$n=-1$

17) Step1: Distribute negatives

$-1-7x+42+6x=36$
Step2: Solve for $x$
$x=7$

18) Step1: Distribute

$-12x-9+24x+4=43$
Step2: Solve for $x$
$x=2$

19) Step1: Distribute $-4$

$24a-22=-4+24a$
Step2: Conclusion
No solution

20) Step1: Distribute

$-5+25x-40x-10=-12x$
Step2: Solve for $x$
$x=-\frac{5}{11}$

Answer:

1. $x=2$
2. $n=0$
3. $x=-7$
4. $a=0$
5. No solution
6. $p=1$
7. $p=-6$
8. No solution
9. $x=4$
10. $x=0$
11. $p=-6$
12. $x=4$
13. $k=-1$
14. $n=4$
15. $x=9$
16. $n=-1$
17. $x=7$
18. $x=2$
19. No solution
20. $x=-\frac{5}{11}$