\frac{5 x+7}{2}-\frac{3}{4}
Answer (1)
Find a common denominator: Rewrite the fractions with a common denominator of 4.
Combine the numerators: Combine the numerators over the common denominator.
Simplify: Simplify the expression by combining like terms.
The simplified expression is 4 10 x + 11 .
Explanation
Understanding the Problem We are asked to simplify the expression 2 5 x + 7 − 4 3 . To do this, we need to find a common denominator and combine the fractions.
Finding a Common Denominator The least common denominator for 2 and 4 is 4. We rewrite the first fraction with the denominator 4: 2 5 x + 7 = 2 × 2 2 ( 5 x + 7 ) = 4 10 x + 14
Rewriting the Expression Now we can rewrite the original expression with the common denominator: 2 5 x + 7 − 4 3 = 4 10 x + 14 − 4 3
Combining the Numerators Combine the numerators: 4 10 x + 14 − 4 3 = 4 10 x + 14 − 3 = 4 10 x + 11
Final Answer The simplified expression is 4 10 x + 11 .
Examples
Simplifying algebraic expressions is a fundamental skill in algebra. For example, if you are calculating the total cost of items with a discount, you might need to simplify an expression like this to find the final price. Suppose you have an initial cost represented by 2 5 x + 7 and then you receive a discount of 4 3 . Simplifying the expression helps you find the net cost after the discount, making it easier to manage your finances or understand pricing models.
