Match the equation with its solution.(3 points)
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2i+3=2i−5
3(2i−7)=6i−21
3i+2i−4=18i
2i+3=2i-5 - No solution
3(2i-7)=6i-21 - i = -3
3i+2i-4=18i - i = -1
To match the equations with their solutions, let's analyze each equation step-by-step.
1) 2i + 3 = 2i - 5
To solve this equation, we can start by isolating the variable. Let's move the terms with i to one side:
2i - 2i + 3 = -5
Simplifying this equation, we get:
3 = -5
From this step, we can see that the equation has no solution. The solution to this equation is "No solution."
2) 3(2i - 7) = 6i - 21
To solve this equation, let's distribute the 3 on the left side:
6i - 21 = 6i - 21
This equation suggests that both sides of the equation are equal. Therefore, the solution of this equation is "All real numbers" or "Infinite solutions," which means any value can satisfy this equation.
3) 3i + 2i - 4 = 18i
Let's combine the like terms first:
5i - 4 = 18i
Next, let's isolate the variable by moving all terms with i to one side:
5i - 18i = 4
Simplifying this equation, we have:
-13i = 4
To solve for i, divide both sides by -13:
i = -4/13
Therefore, the solution to this equation is "i = -4/13."
To summarize, the matching between the equations and their solutions is as follows:
1) 2i + 3 = 2i - 5 - No solution
2) 3(2i - 7) = 6i - 21 - All real numbers or infinite solutions
3) 3i + 2i - 4 = 18i - i = -4/13