Explanation:
We need to solve each of the 8 two-step equations. A two-step equation means we’ll usually do two things:
1. Undo addition or subtraction (move constants to the other side).
2. Undo multiplication or division (isolate x by dividing or multiplying).
Let’s solve each one carefully.
---
1. $0.2x + 0.4 = 0.8$
Step 1: Subtract 0.4 from both sides:
$0.2x = 0.8 - 0.4 = 0.4$
Step 2: Divide both sides by 0.2:
$x = \frac{0.4}{0.2} = 2$
✔ Check: $0.2(2) + 0.4 = 0.4 + 0.4 = 0.8$ ✔️
---
2. $0.2x - 0.14 = 0.3$
Step 1: Add 0.14 to both sides:
$0.2x = 0.3 + 0.14 = 0.44$
Step 2: Divide by 0.2:
$x = \frac{0.44}{0.2} = 2.2$
✔ Check: $0.2(2.2) - 0.14 = 0.44 - 0.14 = 0.3$ ✔️
---
3. $0.6x - 0.7 = 0.5$
Step 1: Add 0.7:
$0.6x = 0.5 + 0.7 = 1.2$
Step 2: Divide by 0.6:
$x = \frac{1.2}{0.6} = 2$
✔ Check: $0.6(2) - 0.7 = 1.2 - 0.7 = 0.5$ ✔️
---
4. $1.2 = 0.5x - 1.8$
Rewrite as: $0.5x - 1.8 = 1.2$
Step 1: Add 1.8:
$0.5x = 1.2 + 1.8 = 3.0$
Step 2: Divide by 0.5:
$x = \frac{3.0}{0.5} = 6$
✔ Check: $0.5(6) - 1.8 = 3 - 1.8 = 1.2$ ✔️
---
5. $0.11x - 0.02 = 0.2$
Step 1: Add 0.02:
$0.11x = 0.2 + 0.02 = 0.22$
Step 2: Divide by 0.11:
$x = \frac{0.22}{0.11} = 2$
✔ Check: $0.11(2) - 0.02 = 0.22 - 0.02 = 0.2$ ✔️
---
6. $1.6 = 0.2x - 1.2$
Rewrite: $0.2x - 1.2 = 1.6$
Step 1: Add 1.2:
$0.2x = 1.6 + 1.2 = 2.8$
Step 2: Divide by 0.2:
$x = \frac{2.8}{0.2} = 14$
✔ Check: $0.2(14) - 1.2 = 2.8 - 1.2 = 1.6$ ✔️
---
7. $0.6 + 0.2x = 1.2$
Step 1: Subtract 0.6:
$0.2x = 1.2 - 0.6 = 0.6$
Step 2: Divide by 0.2:
$x = \frac{0.6}{0.2} = 3$
✔ Check: $0.6 + 0.2(3) = 0.6 + 0.6 = 1.2$ ✔️
---
8. $0.3x - 1.5 = 1.8$
Step 1: Add 1.5:
$0.3x = 1.8 + 1.5 = 3.3$
Step 2: Divide by 0.3:
$x = \frac{3.3}{0.3} = 11$
✔ Check: $0.3(11) - 1.5 = 3.3 - 1.5 = 1.8$ ✔️
All answers verified.
Final Answer:
x = 2, 2.2, 2, 6, 2, 14, 3, 11
Parent Tip: Review the logic above to help your child master the concept of solving equations with decimals worksheet.
