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To determine if the two expressions are equivalent, we can simplify each expression and check if the results are the same.
Let's first simplify the expression 2(x−1)+18:
2(x−1) can be expanded using the distributive property:
2x − 2.
So, the simplified expression is:
2(x−1) + 18 = 2x − 2 + 18 = 2x + 16.
Now, let's simplify the expression 6(x+3)−4x−6:
6(x+3) can be expanded using the distributive property:
6x + 18.
So, the simplified expression is:
6(x+3)−4x−6 = 6x + 18 − 4x − 6 = 2x + 12.
Now we can compare the simplified expressions:
2(x−1)+18 = 2x + 16
6(x+3)−4x−6 = 2x + 12
Both simplified expressions are 2x + a constant term. The constant term is different in each expression (16 in the first and 12 in the second), which means the expressions are not equivalent.
Therefore, 2(x−1)+18 is not equivalent to 6(x+3)−4x−6.