Solving Equations with Fractions
1/2 x - 1/3 x = 7/3
solve for X
i need help
step by step process anyone?
1/2 x - 1/3 x = 7/3
3/6x - 2/6x = 7/3
1/6x = 7/3
x = (7/3) / (1/6)
x = (7/3) * (6/1)
x = 42/3 = 14
To solve the equation 1/2x - 1/3x = 7/3 for x, we can follow these step-by-step instructions:
Step 1: To eliminate the fractions, we need to find a common denominator. In this case, we can use the least common denominator (LCD) of 6.
Multiplying each term by 6, we get:
6 * (1/2x) - 6 * (1/3x) = 6 * (7/3)
(6/2)x - (6/3)x = 42/3
Simplifying, we have:
3x - 2x = 42/3
Step 2: Combine like terms on the left side of the equation.
3x - 2x = 42/3
x = 42/3
Step 3: Simplify the fraction on the right side.
The fraction 42/3 can be simplified by dividing both the numerator and denominator by their greatest common divisor.
The greatest common divisor (GCD) of 42 and 3 is 3.
So, dividing 42 by 3 and 3 by 3, we get:
x = 14/1
Step 4: Simplify the fraction further, if necessary.
The fraction 14/1 can be simplified to just 14.
Therefore, the solution to the equation is:
x = 14
To solve the equation (1/2)x - (1/3)x = 7/3, you need to simplify and combine like terms to isolate x on one side of the equation. Here's a step-by-step process to solve the equation:
Step 1: Find a common denominator
To combine the fractions, you need to find a common denominator for 1/2 and 1/3. In this case, the least common multiple (LCM) of 2 and 3 is 6. Therefore, rewrite the equation with fractions with denominators of 6:
(3/6)x - (2/6)x = 7/3
Step 2: Combine like terms
With the fractions having the same denominator, you can now combine them by subtracting the numerators:
(3x - 2x)/6 = 7/3
Simplifying further:
x/6 = 7/3
Step 3: Isolate x
To solve for x, you need to isolate it. Multiply both sides of the equation by the denominator of x, which is 6:
(6/1)(x/6) = (7/3)(6/1)
Simplifying:
x = 42/3
Step 4: Reduce the fraction
To simplify the solution, you can reduce the fraction 42/3. Both numbers are divisible by 3:
x = 14/1
Therefore, the solution to the equation (1/2)x - (1/3)x = 7/3 is x = 14.