Question

Evaluate the expression. \(-6+(-14)+8\)

Short answer

The evaluation of the expression \(-6+(-14)+8\) is -12.

Step-by-step solution

Identify Numbers

The first thing to do is to identify the numbers in the expression. The numbers in this expression are -6, -14, and 8.

Adding First Two Numbers

Next, adding the first two numbers, -6 and -14 will give \(-6 - 14 = -20\). The negative symbol before 14 means it is a negative number, so it gets subtracted.

Adding Result to Last Number

Now, add the result from step 2 to the last number 8. This gives \(-20 + 8 = -12\). Again, treat 8 as a positive number and subtract it from -20.

Key concepts

Combining Like Terms

When solving algebraic expressions, it is crucial to combine like terms to simplify the problem and find the solution. Like terms are terms that have identical variable parts, such as the same variable raised to the same power. In expressions without variables, like terms are just the numbers. For example, in an expression like \(3x + 2x - x\), we combine the like terms that include the variable \(x\), yielding \(4x\). In the given problem, \( -6, -14, \text{and} 8\) are all like terms because they are constants without variables.

To simplify the expression \( -6 + (-14) + 8\), we combine these like terms by adding and subtracting numbers, following the rules of arithmetic for negative and positive numbers. This method of combining like terms is foundational in algebra and helps students to solve more complex problems efficiently.

Negative Numbers Arithmetic

Understanding how to work with negative numbers is essential in algebra. In arithmetic with negative numbers, remember these core rules: when you add a negative number, it is the same as subtracting its positive counterpart, and when you subtract a negative number, it is the same as adding its positive counterpart.

Let us apply these rules to the example \( -6 + (-14) + 8\). When adding \( -6 \text{and} -14\), you are essentially adding two negative numbers, which equates to moving further into negative territory. So, \( -6 \text{and} -14\) combine to give \( -20\). Adding \(8\), a positive number, to \( -20\) means you move back towards positive territory but still remain in the negatives, resulting in \( -12\). Mastering negative numbers arithmetic will greatly aid in simplifying and solving algebraic expressions.

Algebraic Expressions

Algebraic expressions are collections of numbers, variables, and operations such as addition and subtraction that represent a specific value. Unlike an equation, an algebraic expression doesn't have an equality sign. Evaluating algebraic expressions involves finding the value of the expression by performing the operations in the correct order.

In our case, the expression doesn't have any variables, so we simply follow the order of operations, which in this case is straightforward since there are only addition and subtraction. Remember, there's no need to consider the order of operations (PEMDAS/BODMAS) as there are no parentheses, exponents, multiplication, or division to deal with in our example. With practice, students can learn to quickly evaluate algebraic expressions and solve more intricate algebra problems.