Question

Remove parentheses and simplify. $$(2 x+5)+(x-2)$$

Short answer

Removing the parentheses and simplifying, the expression becomes: \(3x + 3\).

Step-by-step solution

- Remove Parentheses

Since there are no mathematical operations that need to be performed on the terms within the parentheses, simply remove them and write down all terms in a single expression.

- Combine Like Terms

Group and add the coefficients of the terms with the same variable, which is 'x' in this case, and also combine the constant terms.

- Write the Simplified Expression

After combining like terms, write down the simplified expression which represents the sum of the provided expressions.

Key concepts

Combine Like Terms

Combining like terms is an essential process in algebra that simplifies expressions and helps to solve equations more easily. Like terms are terms that have the exact same variable raised to the same power. For example, in the expression \(2x + 5 + x - 2\)\), \(2x\) and \(x\) are like terms because they both contain the variable \(x\) raised to the power of one. To combine them, you simply add their coefficients together, giving you \(2x + x = 3x\).

Likewise, the numbers \(5\) and \(-2) are like terms as well, as they are both constant terms without variables. Combining these gives you \(5 + (-2) = 3\). As a result, the original expression \(2x + 5 + x - 2\) simplifies to \(3x + 3\) when you combine like terms. Remember, the key is to look for terms with the same variables and the same exponents, and then add or subtract their coefficients as required.

Algebraic Simplification Steps

Simplification in algebra often involves a set of steps that, when followed in order, can make complex expressions more manageable. The systematic process involves first removing any parentheses, then combining like terms, and finally arranging the terms in a way that's easy to understand, usually in descending order of the powers of the variables.

In the given exercise, the simplification steps are clear and methodical. You begin by addressing the parentheses, followed by grouping like terms, and finishing with the simplified expression. It's crucial to take these steps one at a time to avoid errors and to keep the process of simplification as clear as possible. By sticking to these steps, even the most complex expressions can be broken down in a systematic and less intimidating way.

Removing Parentheses in Algebra

Parentheses in algebraic expressions denote operations that should be performed first, according to the order of operations (PEMDAS/BODMAS). However, when there are no operations to be performed within the parentheses, as in \(2x + 5\) and \(x - 2\), they can simply be removed, and the expression can be written as a single linear expression. This step is the starting point of simplification.

To remove the parentheses effectively, pay attention to any signs that precede them. If there's a negative sign before a parenthesis, it means you need to distribute the negative sign to each term inside. In our example, there is no such sign, thus no distribution is needed. As a general rule, remember that removing parentheses carefully is crucial to maintaining the integrity of the algebraic expression and setting you up for correct simplification.