Question

Solve each equation and verify your solution 2√6 + 5𝑥 − 2 = 3𝑥

Answer 1

To solve the equation 2√6 + 5𝑥 − 2 = 3𝑥, we need to isolate the variable 𝑥 on one side of the equation.

First, we can move the 5𝑥 term to the other side by subtracting 5𝑥 from both sides:

2√6 - 2 = 3𝑥 - 5𝑥

Next, we can combine like terms on the right side:

2√6 - 2 = -2𝑥

To isolate 𝑥, we can divide both sides by -2:

(2√6 - 2)/-2 = 𝑥

Simplifying the left side of the equation:

-√6 + 1 = 𝑥

Therefore, the solution to the equation is 𝑥 = -√6 + 1.

To verify this solution, we can substitute it back into the original equation:

2√6 + 5(-√6 + 1) - 2 = 3(-√6 + 1)

Simplifying both sides of the equation:

2√6 - 5√6 + 5 - 2 = -3√6 + 3

Combining like terms:

-3√6 + 3 = -3√6 + 3

Since the left side of the equation equals the right side, we can conclude that 𝑥 = -√6 + 1 is indeed a valid solution.