write an equivalent equation that does not contain fractions then solve the equation
2/3x + 1 = 1/2
multiply every term by 6, the LCM
4x + 6 = 3 <--- the "equivalent" equation asked for
4x = -3
x = -3/4
To write an equivalent equation that does not contain fractions, we can start by getting rid of the denominators.
The denominator of the first fraction is 3, so we can multiply the entire equation by 3 to eliminate it. Multiplying both sides by 3 gives us:
3 * (2/3x + 1) = 3 * (1/2)
Simplifying this equation, we have:
2x + 3 = 3/2
Next, we can eliminate the fraction on the right side of the equation. The denominator of the fraction is 2, so we can multiply the equation by 2 to cancel it out. Multiplying both sides by 2 gives us:
2 * (2x + 3) = 2 * (3/2)
Simplifying this equation further, we have:
4x + 6 = 3
Now, we have an equation without any fractions. To solve for x, we need to isolate the variable. Let's start by subtracting 6 from both sides:
4x + 6 - 6 = 3 - 6
This simplifies to:
4x = -3
Finally, we can solve for x by dividing both sides of the equation by 4:
4x/4 = -3/4
This gives us:
x = -3/4
So, the solution to the equation 2/3x + 1 = 1/2, written without fractions, is x = -3/4.