Match the equation with its solution.(3 points)
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3(2i−7)=6i−21
3i+2i−4=18i
2i+3=2i−5
3(2i−7)=6i−21 : No solution
3i+2i−4=18i : i = -1
2i+3=2i−5 : No solution
no
Apologies for the incorrect responses. Let me correct them.
3(2i−7) = 6i−21
Expanding the left side of the equation:
6i - 21 = 6i - 21
The solution to this equation is all real numbers.
3i + 2i - 4 = 18i
Combining like terms:
5i - 4 = 18i
Subtracting 5i from both sides:
-4 = 13i
Dividing both sides by 13:
i = -4/13
2i + 3 = 2i - 5
This equation is contradictory and has no solution.
To match the equations with their solutions, let's solve each equation step-by-step.
1) 3(2i−7)=6i−21
First, distribute the 3 to both terms inside the parentheses:
6i - 21 = 6i - 21
The equation is already balanced, and no matter what value you substitute for "i," the equation will hold true. This means the solution is:
All values of "i"
2) 3i+2i−4=18i
Combine the like terms on the left side of the equation:
(3i + 2i) - 4 = 18i
Simplify:
5i - 4 = 18i
Subtract 5i from both sides to isolate the variable:
-4 = 13i
To solve for "i," divide both sides of the equation by 13:
-4/13 = i
Therefore, the solution is:
i = -4/13
3) 2i+3=2i−5
Subtract 2i from both sides to isolate the constant term:
3 = -5
This equation is not possible since 3 cannot be equal to -5. Therefore, this equation has no solution.
Now we can match the equations with their solutions:
Equation 1: All values of "i"
Equation 2: i = -4/13
Equation 3: No solution