Question

Main

531569
Learning
Solving Equations with the Variable on Both Sides - Item 3458
Practice
Finn shows his work in finding the solution to 4x+6=2+3(x+2). After checking
his answer in the original equation, he found that it did not work.
Where did he make a mistake?

Answer 1

Finn made a mistake in distributing the 3 to the terms inside the parentheses (x+2) on the right side of the equation, resulting in an incorrect solution.

Step-by-step explanation:

Finn made a mistake in distributing the 3 to the terms inside the parentheses (x+2) on the right side of the equation. Let's go step by step to see where he went wrong:

1. Distribute the 3 to the terms inside the parentheses: 4x + 6 = 2 + 3x + 6
2. Combine like terms: 4x + 6 = 3x + 8
3. Move the variable terms to one side and the constant terms to the other: 4x - 3x = 8 - 6
4. Simplify: x = 2

After checking his answer x = 2 in the original equation, 4(2) + 6 does not equal 2 + 3(2) + 6. The left side of the equation equals 14, while the right side equals 16. Therefore, Finn made a mistake in the distribution step, which led to an incorrect solution.

Learn more about Solving Equations with the Variable on Both Sides