Sure, let's solve the equation step by step:
Given equation:
[tex]\[ 12i = 34 - 2(8i + 3) \][/tex]
### Step 1: Distribute the -2 on the right side
First, distribute the -2 to both terms inside the parentheses:
[tex]\[ 2(8i + 3) = 2 \cdot 8i + 2 \cdot 3 = 16i + 6 \][/tex]
Substitute this back into the equation:
[tex]\[ 12i = 34 - (16i + 6) \][/tex]
### Step 2: Simplify the equation
Next, simplify the right side by subtracting [tex]\(16i + 6\)[/tex] from 34:
[tex]\[ 12i = 34 - 16i - 6 \][/tex]
Combine the constants on the right side:
[tex]\[ 12i = 28 - 16i \][/tex]
### Step 3: Move all terms involving [tex]\(i\)[/tex] to one side
Move the term involving [tex]\(i\)[/tex] on the right side to the left side by adding [tex]\(16i\)[/tex] to both sides:
[tex]\[ 12i + 16i = 28 \][/tex]
### Step 4: Combine like terms
Add the coefficients of [tex]\(i\)[/tex] together:
[tex]\[ 28i = 28 \][/tex]
### Step 5: Solve for [tex]\(i\)[/tex]
Finally, divide both sides by 28 to isolate [tex]\(i\)[/tex]:
[tex]\[ i = \frac{28}{28} = 1 \][/tex]
### Conclusion
Thus, the solution to the equation [tex]\(12i = 34 - 2(8i + 3)\)[/tex] is:
[tex]\[ i = 1 \][/tex]
