Match the equation with its solution

Question

2i+3=2i−5_______________

3i+2i−4=18i______________

3(2i−7)=6i−21_________________

Answer 1

Let's solve each equation step-by-step to match them with their solutions.

1. Equation: \( 2i + 3 = 2i - 5 \)

   Solution: Subtract \( 2i \) from both sides: \[ 3 = -5 \]

   This is a contradiction. Therefore, it has no solution.

2. Equation: \( 3i + 2i - 4 = 18i \)

   Solution: Combine like terms on the left: \[ 5i - 4 = 18i \] Now, add \( 4 \) to both sides: \[ 5i = 18i + 4 \] Subtract \( 18i \) from both sides: \[ -13i = 4 \] Divide by \(-13\): \[ i = -\frac{4}{13} \]

3. Equation: \( 3(2i - 7) = 6i - 21 \)

   Solution: Distribute \( 3 \) on the left: \[ 6i - 21 = 6i - 21 \] This simplifies to an identity, which is true for all values of \( i \). Hence, the solution is all real numbers.

Summary of Matching:

• \( 2i + 3 = 2i - 5 \) → No solution
• \( 3i + 2i - 4 = 18i \) → \( i = -\frac{4}{13} \)
• \( 3(2i - 7) = 6i - 21 \) → All real numbers

So, we have:

1. No solution: \( 2i + 3 = 2i - 5 \)
2. \( i = -\frac{4}{13} \): \( 3i + 2i - 4 = 18i \)
3. All real numbers: \( 3(2i - 7) = 6i - 21 \)

Answer 2

no solution

infinte soulution

i = 8

i = 5

i = - 1/3

1 = - 4/13

Answer 3

Let's match the equations with the solutions you've provided.

1. Equation: \( 2i + 3 = 2i - 5 \)

   • This equation simplifies to \( 3 = -5 \), which is a contradiction.
   • Matched Solution: No solution

2. Equation: \( 3(2i - 7) = 6i - 21 \)

   • This simplifies to \( 6i - 21 = 6i - 21 \), which is an identity and true for all values of \( i \).
   • Matched Solution: Infinite solutions

3. Equation: \( 3i + 2i - 4 = 18i \)

   • We previously found that this simplifies to \( -13i = 4 \), giving \( i = -\frac{4}{13} \).
   • This value does not match any of the solutions you provided, which suggests there might be a misunderstanding in the listed solutions.
   • If the provided solutions are i = 8, i = 5, i = -1/3, 1 = -4/13, please note that \( i = -\frac{4}{13} \) is different from those options.

Let’s revise the matches:

1. No solution: \( 2i + 3 = 2i - 5 \)
2. Infinite solutions: \( 3(2i - 7) = 6i - 21 \)
3. \( i = - \frac{4}{13} \) (not matching any from your latest list): \( 3i + 2i - 4 = 18i \)

Summary of solutions:

• \( 2i + 3 = 2i - 5 \) → No solution
• \( 3(2i - 7) = 6i - 21 \) → Infinite solutions
• \( 3i + 2i - 4 = 18i \) → \( i = - \frac{4}{13} \) (which does not match \( i = 8 \), \( i = 5 \), or \( i = -\frac{1}{3} \) from your list)

If you would like to review the equations or clarify the provided solutions, please let me know!

Answer 4

on question 3 which one is correct

Answer 5

Let's carefully solve the third equation step-by-step again:

Equation 3: \( 3(2i - 7) = 6i - 21 \)

1. Distributing \(3\) on the left side: \[ 3(2i) - 3(7) = 6i - 21 \] This simplifies to: \[ 6i - 21 = 6i - 21 \]

2. Now, observe that the left side \(6i - 21\) is equal to the right side \(6i - 21\). This means the equation is true for all values of \( i \).

Conclusion for the third equation:

• Infinite solutions: This equation has infinitely many solutions, meaning any value for \( i \) will satisfy the equation.

Matching to your answers:

From your provided options:

• \( \text{infinite solutions} \) is the match for the third equation.

Summary of all matches:

1. \( 2i + 3 = 2i - 5 \) → No solution
2. \( 3(2i - 7) = 6i - 21 \) → Infinite solutions
3. \( 3i + 2i - 4 = 18i \) → \( i = -\frac{4}{13} \) (again, does not match your provided specific values, which were \( i = 8, i = 5, i = -\frac{1}{3} \))

If you want any further clarification or have a specific number in mind to check, please let me know!

Answer 6

Look at the steps for solving the equation and choose a true statement.

3x−9x+1=2(−3x+1)−1

−6x+1=−6x+2−1

−6x+1=−6x+1

There are infinitely many solutions to the equation.

The only solution to the equation is -6

There are no solutions to the equation.

The only solution to the equation is 1

There is no way to know if there is a solution to the equation.

Answer 7

Let's carefully analyze the equation step-by-step.

Given Equation:

\[ 3x - 9x + 1 = 2(-3x + 1) - 1 \]

Step 1: Simplify the left side \[ 3x - 9x + 1 = -6x + 1 \] So, the left side becomes: \[ -6x + 1 \]

Step 2: Simplify the right side Distributing the \(2\): \[ 2(-3x) + 2(1) - 1 = -6x + 2 - 1 = -6x + 1 \]

Now the equation looks like this: \[ -6x + 1 = -6x + 1 \]

Step 3: Combine both sides Since both sides of the equation are identical: \[ -6x + 1 = -6x + 1 \]

Conclusion:

This is a true statement and an identity, which means it holds for all values of \(x\).

Final Answer:

• There are infinitely many solutions to the equation.

This is the true statement among the options provided.