Simplifying Algebraic Expressions: 5/6(3-x)-1/2(x-4) and 1/3(2x-3)-x
In this article, we will simplify two algebraic expressions: 5/6(3-x)-1/2(x-4) and 1/3(2x-3)-x. These expressions involve fractions, variables, and constants, making them a bit challenging to simplify. Let's break them down step by step.
Simplifying 5/6(3-x)-1/2(x-4)
To simplify this expression, we need to follow the order of operations (PEMDAS):
Step 1: Evaluate the expressions inside the parentheses
5/6(3-x) = 5/6(3) - 5/6x = 5/2 - 5/6x -1/2(x-4) = -1/2x + 2
Step 2: Combine like terms
Now, we can combine the two expressions:
5/2 - 5/6x - 1/2x + 2
Step 3: Simplify the fractions
To simplify the fractions, we can find the least common multiple (LCM) of 2 and 6, which is 6. Then, we can rewrite the fractions with the LCM as the denominator:
5/2 = 15/6 -1/2x = -3/6x -5/6x = -5/6x 2 = 12/6
Step 4: Combine like terms again
Now, we can combine the simplified fractions:
15/6 - 3/6x - 5/6x + 12/6
Step 5: Simplify the expression
Finally, we can simplify the expression by combining like terms:
15/6 - 8/6x + 12/6
Simplifying 1/3(2x-3)-x
To simplify this expression, we can follow the same steps as before:
Step 1: Evaluate the expression inside the parentheses
1/3(2x-3) = 2/3x - 1
Step 2: Write the entire expression
Now, we can write the entire expression:
2/3x - 1 - x
Step 3: Combine like terms
To combine like terms, we can rewrite the expression with the variable x on one side:
2/3x - x - 1
Step 4: Simplify the fractions
We can simplify the fraction by finding the least common multiple (LCM) of 1 and 3, which is 3. Then, we can rewrite the fraction with the LCM as the denominator:
x = 3/3x -1 = -3/3
Step 5: Simplify the expression
Finally, we can simplify the expression by combining like terms:
2/3x - 1/3x - 3/3
= -1/3x - 1
There you have it! We have successfully simplified the two algebraic expressions: 5/6(3-x)-1/2(x-4) and 1/3(2x-3)-x.
