what are the answers to the following problems:

Question

Problem 1: 3(2i+7)=6i+21
Problem 2: 3i+5=2i−7
Problem 3: 3i+2i−7=18
Problem 4: 3(2i−7)=15
Problem 5: 3i+5=3i+7

Answer 1

Let's solve each problem step by step.

Problem 1:
$$3(2i+7)=6i+21$$

Distributing on the left side: $$6i+21=6i+21$$

Both sides are equal, so the equation holds for all values of $i$. The answer is true for all $i$.

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Problem 2:
$$3i+5=2i-7$$

Subtracting $2i$ from both sides: $$3i-2i+5=-7$$ This simplifies to: $$i+5=-7$$

Subtracting 5 from both sides: $$i=-12$$

So, the solution is $i=-12$.

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Problem 3:
$$3i+2i-7=18$$

Combining like terms: $$5i-7=18$$

Adding 7 to both sides: $$5i=25$$

Dividing both sides by 5: $$i=5$$

So, the solution is $i=5$.

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Problem 4:
$$3(2i-7)=15$$

Distributing on the left side: $$6i-21=15$$

Adding 21 to both sides: $$6i=36$$

Dividing both sides by 6: $$i=6$$

So, the solution is $i=6$.

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Problem 5:
$$3i+5=3i+7$$

Subtracting $3i$ from both sides: $$5=7$$

This is not true, so the equation has no solution.

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To summarize:

• Problem 1: True for all $i$
• Problem 2: $i=-12$
• Problem 3: $i=5$
• Problem 4: $i=6$
• Problem 5: No solution.