\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 fractions: Subtract the fractions by combining the numerators over the common denominator.
Simplify the numerator: Combine like terms in the numerator.
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 . This involves combining two fractions by finding a common denominator and then simplifying the resulting expression.
Finding a Common Denominator To combine the fractions, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. We rewrite the first fraction with the denominator of 4: 2 5 x + 7 = 2 × 2 2 ( 5 x + 7 ) = 4 10 x + 14
Combining the Fractions Now we can subtract the second fraction from the first: 4 10 x + 14 − 4 3 = 4 ( 10 x + 14 ) − 3
Simplifying the Numerator Simplify the numerator by combining like terms: 4 10 x + 14 − 3 = 4 10 x + 11
Examples
Simplifying algebraic expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are calculating the total cost of items with a discount and sales tax, you might need to simplify an expression to find the final price. Similarly, in physics, simplifying expressions is crucial for solving equations related to motion, energy, and other concepts. This skill also helps in optimizing processes in engineering and computer science.
