Are the following expressions equivalent? Prove your answer.
5(3x+2) and 15x+10
5(3x+2) = 15x + 10
Thanks :)
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To prove if the two expressions, 5(3x+2) and 15x+10, are equivalent, we need to simplify both expressions and check if they are identical.
Let's start with the expression 5(3x+2):
To simplify this expression, we need to apply the distributive property of multiplication over addition. We multiply the 5 with both terms inside the parentheses:
5(3x+2) = 5*3x + 5*2
Simplifying further:
5(3x+2) = 15x + 10
Now let's compare this with the given expression 15x+10:
From the simplification of the previous expression, we found that it is equivalent to 15x + 10.
Therefore, we have proved that the two expressions, 5(3x+2) and 15x+10, are indeed equivalent.