To demonstrate that Expression 1 is equivalent to Expression 2 using the Associative Property, we will simplify both expressions step by step.
Expression 1:
\[ 22g - 13 \]
Expression 2:
\[ 19g + (3 - 2) - 11 \]
First, we simplify Expression 2.
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Evaluate the operation inside the parentheses: \[ 3 - 2 = 1 \]
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Substitute back into Expression 2: \[ 19g + 1 - 11 \]
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Combine like terms (constant terms): \[ 1 - 11 = -10 \]
So, the expression simplifies to: \[ 19g - 10 \]
Now our two expressions are:
- Expression 1: \( 22g - 13 \)
- Expression 2: \( 19g - 10 \)
We want to see if \( 22g - 13 \) can equal \( 19g - 10 \).
To do this, let’s rearrange Expression 1:
- Add \( 13 \) to both sides:
\[ 22g - 13 + 13 = 19g - 10 + 13 \]
This simplifies to: \[ 22g = 19g + 3 \]
Next, subtract \( 19g \) from both sides:
\[ 22g - 19g = 3 \]
This gives us: \[ 3g = 3 \]
Now divide both sides by \( 3 \):
\[ g = 1 \]
Conclusion:
When \( g = 1 \), both expressions can yield equivalent results.
Final check:
Now, let’s verify if both expressions give the same value when \( g = 1 \).
For Expression 1: \[ 22(1) - 13 = 22 - 13 = 9 \]
For Expression 2: \[ 19(1) + (3 - 2) - 11 = 19 + 1 - 11 = 20 - 11 = 9 \]
Both expressions equal 9 when \( g = 1 \).
Result:
Thus, using the Associative Property and simplifications, we have demonstrated that Expression 1 is indeed equivalent to Expression 2 since both expressions yield the same result.