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3(2i+7) = 6i + 21

Match the equation with its solution.

9 answers

Let's solve the equation \(3(2i + 7) = 6i + 21\) step by step to confirm whether it's accurate.

  1. Distribute the 3 on the left side of the equation:

\[ 3(2i) + 3(7) = 6i + 21 \]

This simplifies to:

\[ 6i + 21 = 6i + 21 \]

  1. Now, we see that both sides of the equation are identical:

\[ 6i + 21 = 6i + 21 \]

This means that the equation is true for all values of \(i\).

Thus, the equation is an identity, meaning it holds true for any \(i\).

The solution to the equation \(3(2i + 7) = 6i + 21\) is that it is valid for all \(i\).

If there are specific solutions you want to match with, please provide them!

so are there infinite solutions?

Yes, that's correct! The equation \(3(2i + 7) = 6i + 21\) simplifies to the identity \(6i + 21 = 6i + 21\). Since both sides are identical for all values of \(i\), this means that the equation is true for every possible value of \(i\).

Therefore, there are indeed infinitely many solutions—every value of \(i\) is a solution to the equation.

3i + 2i - 7 = 18
Match the equation with it's solution

Let's solve the equation \(3i + 2i - 7 = 18\) step by step:

  1. Combine like terms on the left side:

\[ (3i + 2i) - 7 = 18 \]

This simplifies to:

\[ 5i - 7 = 18 \]

  1. Next, add 7 to both sides to isolate the term with \(i\):

\[ 5i - 7 + 7 = 18 + 7 \]

This gives:

\[ 5i = 25 \]

  1. Now, divide both sides by 5 to solve for \(i\):

\[ i = \frac{25}{5} = 5 \]

So, the solution to the equation \(3i + 2i - 7 = 18\) is:

\[ i = 5 \]

If you have specific solutions or options to match, please provide them! Otherwise, \(i = 5\) is the solution to this equation.

3i + 5 = 3i + 7
Match the equation with it's solution

Let's analyze the equation \(3i + 5 = 3i + 7\).

  1. Start by subtracting \(3i\) from both sides to simplify:

\[ 3i + 5 - 3i = 3i + 7 - 3i \]

This simplifies to:

\[ 5 = 7 \]

Since \(5\) does not equal \(7\), this equation is a contradiction.

Conclusion: The equation \(3i + 5 = 3i + 7\) has no solution. It is inconsistent.

If you have any further options or specific solutions to match, please let me know!

3(2i - 7) = 15
Match the equation with it's solution

Let's solve the equation \(3(2i - 7) = 15\) step by step:

  1. Distribute the \(3\) on the left side:

\[ 3(2i) - 3(7) = 15 \]

This simplifies to:

\[ 6i - 21 = 15 \]

  1. Next, add \(21\) to both sides to isolate the term with \(i\):

\[ 6i - 21 + 21 = 15 + 21 \]

This gives:

\[ 6i = 36 \]

  1. Now, divide both sides by \(6\) to solve for \(i\):

\[ i = \frac{36}{6} = 6 \]

So the solution to the equation \(3(2i - 7) = 15\) is:

\[ i = 6 \]

If you have specific solutions or options to match, please provide them! Otherwise, the solution for this equation is \(i = 6\).