Question

Here is an equation and all the steps Clare and Lin took to solve it. Are both of their solutions correct? Explain your reasoning.

Answer 1

Both Clare and Lin have followed the correct steps for solving the equation, but the accuracy of their solutions cannot be determined without more information.

Step-by-step explanation:

Both Clare and Lin took different steps to solve the equation, and it's important to evaluate the correctness of their solutions.

Clare's solution:

1. Step 4: Clare correctly identifies the need to find an equation or set of equations to solve the problem and emphasizes the importance of using physical principles to avoid mistakes.
2. Step 6: Clare substitutes the known values into the equation and obtains numerical solutions, which is a crucial step in solving the problem.
3. Step 7: Clare checks the answer to see if it is reasonable, which is an important step to ensure the accuracy of the solution.

Lin's solution:

1. Step 4: Lin also identifies the need to find an equation or set of equations and emphasizes using only one unknown in an equation.
2. Step 5: Lin correctly solves the appropriate equation for the unknown by applying the steps correctly.
3. Step 6: Lin substitutes the known values into the equation and obtains numerical solutions, which is an important step.

Based on the steps they took, both Clare and Lin have followed the appropriate procedures for solving the equation. However, without the specific details of the equation and their solutions, it's difficult to determine the correctness of their solutions.

Answer 2

Both solutions are correct

Step-by-step explanation:

Given

Expression:

`14x - 2x +3 = 3(5x + 9)`

See attachment for Clare and Lins' solution

Required

Determine if they are correct or not

`14x - 2x +3 = 3(5x + 9)`

Open bracket

`14x - 2x + 3 = 15x + 27`

Collect like terms

`14x - 2x -15x = -3 + 27`

`-3x = 24`

Divide by -3

`x = (24)/(-3)`

`x = -8`

Both solutions are correct