9 answers
To solve the equation \( 3i + 2i - 7 = 18 \), we start by simplifying the left side.
Combine the like terms (the terms with \( i \)):
\[ 3i + 2i = 5i \]
So the equation simplifies to:
\[ 5i - 7 = 18 \]
Next, we'll isolate \( 5i \) by adding 7 to both sides:
\[ 5i = 18 + 7 \]
This simplifies to:
\[ 5i = 25 \]
Now, divide both sides by 5 to solve for \( i \):
\[ i = \frac{25}{5} = 5 \]
Thus, the solution is:
\[ i = 5 \]
To solve the equation \( 3i + 5 = 2i - 7 \), we will isolate \( i \) by following these steps:
\[ 3i - 2i + 5 = -7 \]
\[ i + 5 = -7 \]
\[ i = -7 - 5 \]
\[ i = -12 \]
Thus, the solution to the equation \( 3i + 5 = 2i - 7 \) is:
\[ i = -12 \]
To solve the equation \( 3i + 5 = 3i + 7 \), we start by trying to isolate \( i \).
\[ 3i + 5 - 3i = 3i + 7 - 3i \]
This simplifies to:
\[ 5 = 7 \]
Thus, the conclusion is that there is no solution to the equation \( 3i + 5 = 3i + 7 \).
To solve the equation \( 3(2i + 7) = 6i + 21 \), we first simplify the left side:
\[ 3(2i) + 3(7) = 6i + 21 \]
This simplifies to:
\[ 6i + 21 = 6i + 21 \]
\[ 6i + 21 = 6i + 21 \]
This means that the equation is true for all values of \( i \).
Thus, the solution is that there are infinitely many solutions, or we can say all values of \( i \) are solutions.
To solve the equation \( 3(2i - 7) = 15 \), follow these steps:
\[ 3 \cdot 2i - 3 \cdot 7 = 15 \]
This simplifies to:
\[ 6i - 21 = 15 \]
\[ 6i - 21 + 21 = 15 + 21 \]
This simplifies to:
\[ 6i = 36 \]
\[ i = \frac{36}{6} = 6 \]
Thus, the solution to the equation \( 3(2i - 7) = 15 \) is:
\[ i = 6 \]
