Problem 56
Question
\(16-5 m-4 m-2+2 m\) 56\. \(6-3 z-2 z-5-2 z\)
Step-by-Step Solution
Verified Answer
14 - 7m; 1 - 7z
1Step 1: Simplify the first expression
Combine the like terms in the expression: \(16-5m-4m-2+2m\).
2Step 2: Combine the constants
Add the constants: \(16-2 = 14\).
3Step 3: Combine the variable terms
Combine the coefficients of \(m\): \(-5m-4m+2m = -7m\).
4Step 4: Write the simplified expression
The simplified expression is: \(14 - 7m\).
5Step 5: Simplify the second expression
Combine the like terms in the expression: \(6-3z-2z-5-2z\).
6Step 6: Combine the constants
Add the constants: \(6-5 = 1\).
7Step 7: Combine the variable terms
Combine the coefficients of \(z\): \(-3z-2z-2z = -7z\).
8Step 8: Write the simplified expression
The simplified expression is: \(1 - 7z\).
Key Concepts
Simplifying ExpressionsAlgebraic ExpressionsCoefficients
Simplifying Expressions
Simplifying expressions is key in algebra. It means reducing an expression to its simplest form by combining like terms.
An algebraic expression has numbers, variables, and operations (like addition and subtraction). By simplifying, you make the expression easier to work with.
Here's what you should do:
- Identify and group like terms (terms that have the same variable raised to the same power).
- Add or subtract the coefficients of these like terms.
- Combine the constants (numbers without variables).
A simplified expression is cleaner and easier to read.
An algebraic expression has numbers, variables, and operations (like addition and subtraction). By simplifying, you make the expression easier to work with.
Here's what you should do:
- Identify and group like terms (terms that have the same variable raised to the same power).
- Add or subtract the coefficients of these like terms.
- Combine the constants (numbers without variables).
A simplified expression is cleaner and easier to read.
Algebraic Expressions
An algebraic expression can seem complex, but it's just a mix of numbers, variables, and operations.
For example, in the expression: \(16-5m-4m-2+2m\), you'll find:
- Constants: Numbers like 16 and -2.
- Variables: Symbols like \(m\) that represent unknown values.
- Coefficients: Numbers before variables showing how many times the variable is multiplied.
In algebra, the goal is often to simplify these expressions. By knowing what each part represents, you can focus on combining like terms and making the expression simpler.
For example, in the expression: \(16-5m-4m-2+2m\), you'll find:
- Constants: Numbers like 16 and -2.
- Variables: Symbols like \(m\) that represent unknown values.
- Coefficients: Numbers before variables showing how many times the variable is multiplied.
In algebra, the goal is often to simplify these expressions. By knowing what each part represents, you can focus on combining like terms and making the expression simpler.
Coefficients
Coefficients are the numerical part of terms with variables. They tell you how many times to use the variable in a term.
For instance, in the term \(-5m\), -5 is the coefficient. It means \(-5\text{ times }m\).
While simplifying expressions, you need to combine coefficients of like terms.
For example, combine \(-5m, -4m, \text{ and } 2m\) to get: \(-5 - 4 + 2 = -7\).
Eventually, the expression: \(-5m - 4m + 2m\) becomes: \(-7m\).
Understanding coefficients makes it easier to combine like terms and simplify expressions effectively.
For instance, in the term \(-5m\), -5 is the coefficient. It means \(-5\text{ times }m\).
While simplifying expressions, you need to combine coefficients of like terms.
For example, combine \(-5m, -4m, \text{ and } 2m\) to get: \(-5 - 4 + 2 = -7\).
Eventually, the expression: \(-5m - 4m + 2m\) becomes: \(-7m\).
Understanding coefficients makes it easier to combine like terms and simplify expressions effectively.