Let's solve each of the
simple linear equations step by step. The goal is to isolate the variable on one side of the equation.
---
1. $ 3b + 9 = -18 $
Subtract 9 from both sides:
$$
3b = -18 - 9 = -27
$$
Divide by 3:
$$
b = \frac{-27}{3} = -9
$$
✔ Answer: $ b = -9 $
---
2. $ 3v + 1 = 22 $
Subtract 1:
$$
3v = 21
$$
Divide by 3:
$$
v = 7
$$
✔ Answer: $ v = 7 $
---
3. $ 3y - 2 = 10 $
Add 2:
$$
3y = 12
$$
Divide by 3:
$$
y = 4
$$
✔ Answer: $ y = 4 $
---
4. $ 2z + 1 = 15 $
Subtract 1:
$$
2z = 14
$$
Divide by 2:
$$
z = 7
$$
✔ Answer: $ z = 7 $
---
5. $ -2b - (-7) = 11 $
Simplify: $-(-7) = +7$
$$
-2b + 7 = 11
$$
Subtract 7:
$$
-2b = 4
$$
Divide by -2:
$$
b = -2
$$
✔ Answer: $ b = -2 $
---
6. $ 3c - 9 = -27 $
Add 9:
$$
3c = -18
$$
Divide by 3:
$$
c = -6
$$
✔ Answer: $ c = -6 $
---
7. $ -3c - 4 = 2 $
Add 4:
$$
-3c = 6
$$
Divide by -3:
$$
c = -2
$$
✔ Answer: $ c = -2 $
---
8. $ -3c + 8 = -10 $
Subtract 8:
$$
-3c = -18
$$
Divide by -3:
$$
c = 6
$$
✔ Answer: $ c = 6 $
---
9. $ 2c - 8 = -18 $
Add 8:
$$
2c = -10
$$
Divide by 2:
$$
c = -5
$$
✔ Answer: $ c = -5 $
---
10. $ 3a - 5 = -23 $
Add 5:
$$
3a = -18
$$
Divide by 3:
$$
a = -6
$$
✔ Answer: $ a = -6 $
---
11. $ -2a - 8 = -4 $
Add 8:
$$
-2a = 4
$$
Divide by -2:
$$
a = -2
$$
✔ Answer: $ a = -2 $
---
12. $ 3c - 2 = -26 $
Add 2:
$$
3c = -24
$$
Divide by 3:
$$
c = -8
$$
✔ Answer: $ c = -8 $
---
13. $ 2u + 7 = 5 $
Subtract 7:
$$
2u = -2
$$
Divide by 2:
$$
u = -1
$$
✔ Answer: $ u = -1 $
---
14. $ 3a - (-1) = -5 $
Simplify: $-(-1) = +1$
$$
3a + 1 = -5
$$
Subtract 1:
$$
3a = -6
$$
Divide by 3:
$$
a = -2
$$
✔ Answer: $ a = -2 $
---
15. $ -2u + (-1) = -13 $
Simplify: $+(-1) = -1$
$$
-2u - 1 = -13
$$
Add 1:
$$
-2u = -12
$$
Divide by -2:
$$
u = 6
$$
✔ Answer: $ u = 6 $
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | $ b = -9 $ |
| 2 | $ v = 7 $ |
| 3 | $ y = 4 $ |
| 4 | $ z = 7 $ |
| 5 | $ b = -2 $ |
| 6 | $ c = -6 $ |
| 7 | $ c = -2 $ |
| 8 | $ c = 6 $ |
| 9 | $ c = -5 $ |
|10 | $ a = -6 $ |
|11 | $ a = -2 $ |
|12 | $ c = -8 $ |
|13 | $ u = -1 $ |
|14 | $ a = -2 $ |
|15 | $ u = 6 $ |
Let me know if you'd like these explained in more detail or formatted differently!
Parent Tip: Review the logic above to help your child master the concept of linear systems worksheet.
