Let’s solve each equation one by one, step by step. Remember: isolate the variable (get it alone on one side) by doing the opposite operation.
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1. $ b + 8.6 = 18 $
Subtract 8.6 from both sides:
$ b = 18 - 8.6 = 9.4 $
→ Already shown in image; correct.
2. $ 12.1 = p - 9.3 $
Add 9.3 to both sides:
$ p = 12.1 + 9.3 = 21.4 $
3. $ z + 15.4 = 17 $
Subtract 15.4:
$ z = 17 - 15.4 = 1.6 $
4. $ -35.5 = -5 - x $
First, add 5 to both sides:
$ -35.5 + 5 = -x $ → $ -30.5 = -x $
Multiply both sides by -1:
$ x = 30.5 $
5. $ -28 = -7.3 + a $
Add 7.3 to both sides:
$ a = -28 + 7.3 = -20.7 $
6. $ 12.9 + t = 36 $
Subtract 12.9:
$ t = 36 - 12.9 = 23.1 $
7. $ 47.6 - n = 17 $
Subtract 47.6 from both sides:
$ -n = 17 - 47.6 = -30.6 $
Multiply by -1:
$ n = 30.6 $
8. $ x - 22.3 = 19.5 $
Add 22.3:
$ x = 19.5 + 22.3 = 41.8 $
9. $ -20.7 = 8.3 + b $
Subtract 8.3:
$ b = -20.7 - 8.3 = -29.0 $
10. $ -40 = y - 12.5 $
Add 12.5:
$ y = -40 + 12.5 = -27.5 $
11. $ 39.3 + z = -15 $
Subtract 39.3:
$ z = -15 - 39.3 = -54.3 $
12. $ -26.1 = -11 - p $
Add 11 to both sides:
$ -26.1 + 11 = -p $ → $ -15.1 = -p $
Multiply by -1:
$ p = 15.1 $
Now round all answers to
two decimal places (most are already exact to two decimals, but let’s confirm):
1. $ b = 9.40 $
2. $ p = 21.40 $
3. $ z = 1.60 $
4. $ x = 30.50 $
5. $ a = -20.70 $
6. $ t = 23.10 $
7. $ n = 30.60 $
8. $ x = 41.80 $
9. $ b = -29.00 $
10. $ y = -27.50 $
11. $ z = -54.30 $
12. $ p = 15.10 $
All values are already at most two decimal places — no further rounding needed.
Final Answer:
b = 9.40, p = 21.40, z = 1.60, x = 30.50, a = -20.70, t = 23.10, n = 30.60, x = 41.80, b = -29.00, y = -27.50, z = -54.30, p = 15.10
Parent Tip: Review the logic above to help your child master the concept of solving equations with decimals worksheet.
