Problem 16 - Elementary Algebra

Question

Simplify. $$ -2-32+(-2) 2 $$

Step-by-Step Solution

Answer

-38

Step 1: Simplify multiplication in the expression

First, identify and perform any multiplications in the expression. The expression is -2 - 32 + (-2) 2. Multiply (-2) and 2:\[(-2) \times 2 = -4\]

Step 2: Rewrite the expression

Substitute the result from Step 1 back into the expression. This gives us:\[-2 - 32 + (-4)\]

Step 3: Simplify Addition and Subtraction

Combine the terms by performing the addition and subtraction from left to right:1. \(-2 - 32 = -34\)2. Add \(-4\) to the result: \[-34 + (-4) = -38\]

Step 4: Finalize the simplified result

The final simplified result of the expression is:\[-38\]

Key Concepts

Multiplication and Addition

When faced with an expression that includes multiplication and addition, it is important to tackle each operation correctly. Multiplication, like division, should be handled first according to the order of operations, which we'll discuss later. However, firstly, identify any parts of the expression that require multiplication.
For example, in the expression \(-2 - 32 + (-2) \times 2\),
the multiplication \((-2) \times 2 = -4\) should be done first.
Afterwards, insert the result back into the expression before proceeding to addition.
So, the expression becomes \(-2 - 32 + (-4)\).
By systematically dealing with multiplication before addition, the process of simplifying an expression becomes clearer and more manageable.

Combining Like Terms

To simplify an expression fully, it’s crucial to combine like terms, which are terms that have the same variable factor raised to the same power or are constants. In many arithmetic expressions, you are working only with constants.
After addressing multiplication in our expression \(-2 - 32 + (-4)\),
you then need to combine all the numbers through addition and subtraction.

• Start with \(-2 - 32\), which equals \(-34\).
• Then add \(-4\) to your result to get \(-38\).

Combining like terms makes the expression cleaner and easier to compute by reducing the equation to its simplest terms. By mastering this skill, solving complex equations becomes a breeze.

Order of Operations

The order of operations is a fundamental principle in mathematics that describes the correct sequence in which to solve different parts of a problem. A common acronym for remembering the order is PEMDAS:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

With the expression \(-2 - 32 + (-2) \times 2\), it involves multiplication, subtraction, and addition.
According to PEMDAS, tackle multiplication first: \((-2) \times 2 = -4\).
Then substitute this back and do the addition and subtraction from left to right:
\(-2 - 32 + (-4) = -38\).
Understanding and applying the order of operations ensures that no matter how intricate an expression seems, you can break it down step by step and reach the correct solution.