2√3𝑥 + 1 = 𝑥 + 3
To solve this equation, we want to isolate the variable 𝑥 on one side.
First, we'll start by isolating the term containing 𝑥. We can subtract 𝑥 from both sides of the equation to get:
2√3𝑥 - 𝑥 + 1 = 𝑥 + 3 - 𝑥
Simplifying the equation:
√3𝑥 + 1 = 3
Next, let's isolate √3𝑥 by subtracting 1 from both sides of the equation:
√3𝑥 = 3 - 1
Simplifying further:
√3𝑥 = 2
To isolate 𝑥, we square both sides of the equation to eliminate the square root:
(√3𝑥)² = 2²
Simplifying again:
3𝑥 = 4
Finally, divide both sides of the equation by 3:
𝑥 = 4/3
Therefore, the solution to the equation 2√3𝑥 + 1 = 𝑥 + 3 is 𝑥 = 4/3.
To solve the equation 2√3𝑥 + 1 = 𝑥 + 3, follow these steps:
Step 1: Move all the terms involving 𝑥 to one side of the equation, and move the constant terms to the other side. This can be done by subtracting 𝑥 and adding 1 from both sides of the equation:
2√3𝑥 - 𝑥 = 3 - 1
Simplifying the equation, we get:
√3𝑥 = 2
Step 2: To eliminate the square root, square both sides of the equation:
(√3𝑥)² = 2²
Simplifying the equation, we get:
3𝑥 = 4
Step 3: Divide both sides of the equation by 3 to solve for 𝑥:
𝑥 = 4/3
So, the solution to the equation 2√3𝑥 + 1 = 𝑥 + 3 is 𝑥 = 4/3.
To solve the equation 2√3𝑥 + 1 = 𝑥 + 3, you can start by isolating the term with the variable on one side of the equation.
Step 1: Move the 𝑥 term to the other side by subtracting 𝑥 from both sides of the equation:
2√3𝑥 + 1 - 𝑥 = 𝑥 + 3 - 𝑥
Simplifying the equation:
2√3𝑥 - 𝑥 + 1 = 3
Step 2: Combine like terms:
-𝑥 and 2√3𝑥 cannot be combined because they have different variables.
The equation remains:
2√3𝑥 - 𝑥 + 1 = 3
Step 3: Move the constant to the other side by subtracting 1 from both sides of the equation:
2√3𝑥 - 𝑥 + 1 - 1 = 3 - 1
Simplifying the equation:
2√3𝑥 - 𝑥 = 2
Step 4: Now that you have only one term with the variable on the left side of the equation, you can solve for 𝑥.
In this equation, we have two different terms, 2√3𝑥 and -𝑥, and we can combine them to form a single term by finding the common denominator.
Since 2√3 can be written as 2√(3 * 1), we can multiply the numerator and the denominator by √1 to obtain a common denominator:
2√3𝑥 * √1 / √1 - 𝑥 * √1 / √1 = 2
Simplifying:
2√(3 * 1)𝑥 / √(1 * 1) - 𝑥√(1 * 1) / √(1 * 1) = 2
2√(3 * 1)𝑥 / √1 - 𝑥√(1 * 1) / √1 = 2
2√(3 * 1)𝑥 / 1 - 𝑥√(1 * 1) / 1 = 2
2√3𝑥 / 1 - 𝑥√1 / 1 = 2
2√3𝑥 - 𝑥√1 = 2
Step 5: Simplify the equation:
The square root of 1 is 1, so we have:
2√3𝑥 - 𝑥 = 2
Step 6: Combine like terms:
2√3𝑥 and -𝑥 can be combined because they have the same variable.
The equation becomes:
(2√3 - 1)𝑥 = 2
Step 7: Solve for 𝑥:
To isolate the variable, divide both sides of the equation by (2√3 - 1):
(2√3 - 1)𝑥 / (2√3 - 1) = 2 / (2√3 - 1)
Simplifying:
𝑥 = 2 / (2√3 - 1)
So, the solution to the equation 2√3𝑥 + 1 = 𝑥 + 3 is 𝑥 = 2 / (2√3 - 1).