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1 and 2: Write an equation and solve for the variable.

1. Balance: 23 = y + 12

• Equation: $23 = y + 12$
• Solution: Subtract 12 from both sides: $y = 23 - 12 = 11$

2. Balance: 3 + a = 15

• Equation: $3 + a = 15$
• Solution: Subtract 3 from both sides: $a = 15 - 3 = 12$

3–8: Solve each equation.

3. $g - 8 = 25$

• Add 8 to both sides: $g = 25 + 8 = 33$

4. $25 + y = 42$

• Subtract 25 from both sides: $y = 42 - 25 = 17$

5. $r + 82 = 97$

• Subtract 82 from both sides: $r = 97 - 82 = 15$

6. $30 = m - 18$

• Add 18 to both sides: $m = 30 + 18 = 48$

7. $150 = e + 42$

• Subtract 42 from both sides: $e = 150 - 42 = 108$

8. $a - 51 = 12$

• Add 51 to both sides: $a = 12 + 51 = 63$

9. Analyze and solve the word problem.

a. Explain how $t - 12 = 42$ models the situation.

• $t$ represents the total number of students who tried out for the play.
• $t - 12$ accounts for the number of students who didn’t get a role.
• The equation $t - 12 = 42$ states that 42 students didn’t get a role.

b. Solve for $t$.

• Solve $t - 12 = 42$: $t = 42 + 12 = 54$
• So, $54$ students tried out for the play.

10. Solve $x + 7 = 28$.

• Subtract 7 from both sides: $x = 28 - 7 = 21$

11. Is Krystal correct?

• Krystal says to add to solve $y - 11 = 52$.
• This is correct because to isolate $y$, you add 11 to both sides: $y = 52 + 11 = 63$
• Yes, Krystal is correct.

Would you like a detailed explanation for any part?

Related Questions:

1. How do addition and subtraction equations relate to balancing a scale?
2. Can you apply these concepts to real-world scenarios like budgeting or cooking?
3. How can visual aids like bar diagrams help with solving equations?
4. What’s the importance of verifying solutions after solving equations?
5. Can you derive a word problem based on $a - 51 = 12$?

Tip: Always double-check your final answer by substituting it back into the original equation.