Problem 40
Question
\((7 x+15)-(2 x-3)\)
Step-by-Step Solution
Verified Answer
5x + 18
1Step 1: Identify Like Terms
First, identify the like terms in the expression (7x + 15) - (2x - 3). The like terms are those with the variable x and those that are constants (numbers without variables).
2Step 2: Distribute the Negative Sign
Next, distribute the negative sign across the terms inside the parentheses after the subtraction sign. This gives: 7x + 15 - 2x + 3.
3Step 3: Combine Like Terms
Combine the like terms by adding or subtracting them. For the terms with x: 7x - 2x = 5x. For the constants: 15 + 3 = 18.
4Step 4: Write the Final Expression
Combine the simplified like terms to write the final expression: 5x + 18.
Key Concepts
Like TermsDistributive PropertyCombining Like Terms
Like Terms
When working with algebraic expressions, it is crucial to identify like terms. Like terms have the same variable raised to the same power. For instance, in the expression (7x + 15) - (2x - 3), 7x and 2x are like terms because they both have the variable x. Constants like 15 and -3 are also considered like terms because they do not contain any variables. Identifying like terms helps in simplifying algebraic expressions effectively.
Distributive Property
The distributive property allows you to multiply a single term by each term inside a parenthesis. In the context of subtraction, it means distributing the negative sign across the terms inside the parenthesis. For example, in the expression (7x + 15) - (2x - 3), the negative sign in front of the second parenthesis needs to be distributed. This results in 7x + 15 - 2x + 3. Effectively, each term in (2x - 3) changes sign when the negative is distributed.
Combining Like Terms
Once you have identified and distributed any necessary signs, the next step in simplifying an algebraic expression is to combine like terms. This means to perform the operation of addition or subtraction on the coefficients of like terms. In the expression 7x + 15 - 2x + 3, you combine the terms with x (7x and -2x) separately from the constants (15 and 3). Thus, 7x - 2x becomes 5x and 15 + 3 becomes 18. Combining these results gives the simplified expression 5x + 18.