Let’s solve each equation step by step to determine if it has
one solution,
no solution, or
infinite solutions.
---
13) 4(m - 1) + 5 = -(1 - 4m)
Left side:
4(m - 1) + 5 = 4m - 4 + 5 = 4m + 1
Right side:
-(1 - 4m) = -1 + 4m = 4m - 1
So:
4m + 1 = 4m - 1
Subtract 4m from both sides:
1 = -1 → False!
→
No solution
---
14) -6(k + 1) = -3 - (6k + 3)
Left side:
-6(k + 1) = -6k - 6
Right side:
-3 - (6k + 3) = -3 - 6k - 3 = -6k - 6
So:
-6k - 6 = -6k - 6 → Always true!
→
Infinite solutions
---
15) -21 - 8a = -1 + 6(4 - 5a)
Right side:
6(4 - 5a) = 24 - 30a
So right side: -1 + 24 - 30a = 23 - 30a
Equation:
-21 - 8a = 23 - 30a
Add 30a to both sides:
-21 + 22a = 23
Add 21 to both sides:
22a = 44
Divide by 22:
a = 2
→
One solution
---
16) -7p - 12 = -4p + 3(-4 - p)
Right side:
3(-4 - p) = -12 - 3p
So right side: -4p -12 -3p = -7p -12
Equation:
-7p - 12 = -7p - 12 → Always true!
→
Infinite solutions
---
17) -11 + x = -7x - 8(-x + 1)
Right side:
-8(-x + 1) = 8x - 8
So right side: -7x + 8x - 8 = x - 8
Equation:
-11 + x = x - 8
Subtract x from both sides:
-11 = -8 → False!
→
No solution
---
18) 33 + 6x = 3(-1 + 5x)
Right side:
3(-1 + 5x) = -3 + 15x
Equation:
33 + 6x = -3 + 15x
Subtract 6x:
33 = -3 + 9x
Add 3:
36 = 9x
Divide by 9:
x = 4
→
One solution
---
19) -5(x - 1) = 5 - 5x
Left side:
-5(x - 1) = -5x + 5
Equation:
-5x + 5 = 5 - 5x → Same on both sides!
→
Infinite solutions
---
20) 12 + 4n = 4(n + 3)
Right side:
4(n + 3) = 4n + 12
Equation:
12 + 4n = 4n + 12 → Always true!
→
Infinite solutions
---
21) 208 = 8(1 + 5x)
Divide both sides by 8:
26 = 1 + 5x
Subtract 1:
25 = 5x
Divide by 5:
x = 5
→
One solution
---
22) 4(-4 - 8m) + 28m + 4m = -272
First, expand:
4(-4 - 8m) = -16 - 32m
Now combine all terms on left:
-16 - 32m + 28m + 4m = -16 + 0m = -16
Equation:
-16 = -272 → False!
→
No solution
Wait — let me double-check that.
Left side:
4*(-4) = -16
4*(-8m) = -32m
Then +28m +4m → total m terms: -32m + 28m + 4m = 0m
Constants: -16
So yes: -16 = -272 → Not true.
→
No solution
---
23) 93 + 12m = 3(4m - 1) + 96
Right side:
3(4m - 1) = 12m - 3
Plus 96: 12m - 3 + 96 = 12m + 93
Equation:
93 + 12m = 12m + 93 → Always true!
→
Infinite solutions
---
24) 267 = 5(8n + 4) + 7
Right side:
5(8n + 4) = 40n + 20
Plus 7: 40n + 27
Equation:
267 = 40n + 27
Subtract 27:
240 = 40n
Divide by 40:
n = 6
→
One solution
---
Final Answers:
13) No solution
14) Infinite solutions
15) One solution
16) Infinite solutions
17) No solution
18) One solution
19) Infinite solutions
20) Infinite solutions
21) One solution
22) No solution
23) Infinite solutions
24) One solution
Parent Tip: Review the logic above to help your child master the concept of one solution no solution infinite solutions worksheet.
