Solve each equation and verify your solution 2√6 + 5𝑥 − 2 = 3𝑥
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.
To solve the equation 2√6 + 5𝑥 − 2 = 3𝑥, we need to isolate the variable 𝑥.
First, let's simplify the equation by combining like terms. We have a term with √6, a term with 𝑥, and a constant term.
2√6 + 5𝑥 − 2 = 3𝑥
Next, let's move the terms involving 𝑥 to one side of the equation and the constant terms to the other side. We can achieve this by subtracting 3𝑥 from both sides and adding 2 to both sides.
2√6 + 5𝑥 − 3𝑥 - 2 = 3𝑥 - 3𝑥 + 2
Simplifying further, we get:
2√6 + 2𝑥 - 2 = 2
Now, let's isolate the 𝑥 term by subtracting 2 from both sides.
2√6 + 2𝑥 - 2 - 2 = 2 - 2
The equation becomes:
2√6 + 2𝑥 = 0
To isolate 𝑥, we'll subtract 2√6 from both sides.
2√6 + 2𝑥 - 2√6 = 0 - 2√6
The equation simplifies to:
2𝑥 = -2√6
Finally, to solve for 𝑥, divide both sides of the equation by 2.
𝑥 = -√6
Now, let's verify this solution by substituting 𝑥 = -√6 back into the original equation:
2√6 + 5𝑥 - 2 = 3𝑥
Substituting 𝑥 = -√6 gives us:
2√6 + 5(-√6) - 2 = 3(-√6)
Simplifying both sides:
2√6 - 5√6 - 2 = -3√6
Combining like terms:
-3√6 - 2 = -3√6
Both sides of the equation are equal, so 𝑥 = -√6 is indeed the correct solution. This verifies that our solution is correct.
To solve the equation 2√6 + 5𝑥 − 2 = 3𝑥, we will isolate the variable 𝑥 on one side of the equation.
Step 1: Remove the constant term on the same side as the variable.
Subtracting 5𝑥 from both sides, we have:
2√6 - 2 = 3𝑥 - 5𝑥
Simplifying, we get:
2√6 - 2 = -2𝑥
Step 2: Combine like terms.
The right side of the equation has only one term, -2𝑥.
Step 3: Isolate the variable 𝑥.
We'll divide both sides by -2 to solve for 𝑥:
(2√6 - 2) / -2 = 𝑥
Simplifying further,
-√6 + 1 = 𝑥
So, the solution to the equation 2√6 + 5𝑥 − 2 = 3𝑥 is 𝑥 = -√6 + 1.
To verify the solution, we substitute 𝑥 = -√6 + 1 back into the original equation:
LHS = 2√6 + 5(-√6 + 1) - 2
= 2√6 - 5√6 + 5 - 2
= -3√6 + 3
RHS = 3𝑥
= 3(-√6 + 1)
= -3√6 + 3
Therefore, both sides of the equation equal -3√6 + 3, confirming that 𝑥 = -√6 + 1 is the correct solution.