Question
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Part 1
Determine whether the equation is an identity or whether it has no solution.
2(aminus5)equals4aminus(2aplus10)
Part 1
Determine whether the equation is an identity or whether it has no solution.
2(aminus5)equals4aminus(2aplus10)
Answers
GPT-4o mini
To determine whether the equation \(2(a - 5) = 4a - (2a + 10)\) is an identity or has no solution, we will simplify both sides of the equation and see if we can find a solution or determine if it holds for all values of \(a\).
Starting with the left side:
\[
2(a - 5) = 2a - 10
\]
Now let's simplify the right side:
\[
4a - (2a + 10) = 4a - 2a - 10 = 2a - 10
\]
Now the equation looks like this:
\[
2a - 10 = 2a - 10
\]
Notice that both sides are equal and represent the same expression. This means the equation is always true for any value of \(a\).
Therefore, the equation \(2(a - 5) = 4a - (2a + 10)\) is an identity.
Starting with the left side:
\[
2(a - 5) = 2a - 10
\]
Now let's simplify the right side:
\[
4a - (2a + 10) = 4a - 2a - 10 = 2a - 10
\]
Now the equation looks like this:
\[
2a - 10 = 2a - 10
\]
Notice that both sides are equal and represent the same expression. This means the equation is always true for any value of \(a\).
Therefore, the equation \(2(a - 5) = 4a - (2a + 10)\) is an identity.