Let’s solve each equation one by one. We’ll move all the variable terms (like 12b, 5b) to one side and all the numbers to the other side. Then we’ll simplify and find the value of the letter.
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Equation 1: 12b - 4 = 5b + 6
Step 1: Subtract 5b from both sides
→ 12b - 5b - 4 = 6
→ 7b - 4 = 6
Step 2: Add 4 to both sides
→ 7b = 6 + 4
→ 7b = 10
Step 3: Divide both sides by 7
→ b = 10/7
✔ Final Answer for Equation 1:
b = 10/7
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Equation 2: 14t - 2 = 23t + 5
Step 1: Subtract 14t from both sides
→ -2 = 9t + 5
Step 2: Subtract 5 from both sides
→ -2 - 5 = 9t
→ -7 = 9t
Step 3: Divide both sides by 9
→ t = -7/9
✔ Final Answer for Equation 2:
t = -7/9
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Equation 3: 45x - 12 = x + 56
Step 1: Subtract x from both sides
→ 44x - 12 = 56
Step 2: Add 12 to both sides
→ 44x = 56 + 12
→ 44x = 68
Step 3: Divide both sides by 44
→ x = 68/44 → Simplify by dividing numerator and denominator by 4
→ x = 17/11
✔ Final Answer for Equation 3:
x = 17/11
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Equation 4: 7x - 8 = 1x - 5
(Note: “1x” is just “x”)
Step 1: Subtract x from both sides
→ 6x - 8 = -5
Step 2: Add 8 to both sides
→ 6x = -5 + 8
→ 6x = 3
Step 3: Divide both sides by 6
→ x = 3/6 → Simplify
→ x = 1/2
✔ Final Answer for Equation 4:
x = 1/2
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Equation 5: 34y - 56 = 7y - 2
Step 1: Subtract 7y from both sides
→ 27y - 56 = -2
Step 2: Add 56 to both sides
→ 27y = -2 + 56
→ 27y = 54
Step 3: Divide both sides by 27
→ y = 54/27
→ y = 2
✔ Final Answer for Equation 5:
y = 2
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Equation 6: 45z - 7 = 23 - 5z
Step 1: Add 5z to both sides
→ 50z - 7 = 23
Step 2: Add 7 to both sides
→ 50z = 23 + 7
→ 50z = 30
Step 3: Divide both sides by 50
→ z = 30/50 → Simplify by dividing by 10
→ z = 3/5
✔ Final Answer for Equation 6:
z = 3/5
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Equation 7: 34a - 56 = 7a - 16
Step 1: Subtract 7a from both sides
→ 27a - 56 = -16
Step 2: Add 56 to both sides
→ 27a = -16 + 56
→ 27a = 40
Step 3: Divide both sides by 27
→ a = 40/27
✔ Final Answer for Equation 7:
a = 40/27
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Final Answer:
b = 10/7
t = -7/9
x = 17/11
x = 1/2
y = 2
z = 3/5
a = 40/27
Parent Tip: Review the logic above to help your child master the concept of math worksheet for class 6.
