Simplify the algebraic expression: 5+3c-2c-17
The correct answer and explanation is:
To simplify the algebraic expression 5+3c−2c−175 + 3c – 2c – 17, follow these steps:
- Group like terms: The expression contains both constant terms and variable terms (terms involving cc). The constant terms are 55 and −17-17, and the terms with cc are 3c3c and −2c-2c.
- Simplify the variable terms: Combine the terms with cc (the like terms) together: 3c−2c=1c or simply c3c – 2c = 1c \text{ or simply } c So, the variable part simplifies to cc.
- Simplify the constant terms: Now, combine the constants 55 and −17-17: 5−17=−125 – 17 = -12 So, the constant part simplifies to −12-12.
- Rewrite the expression: After simplifying both parts, the expression becomes: c−12c – 12
Therefore, the simplified form of the expression is c−12c – 12.
Explanation:
In algebra, simplifying an expression involves combining like terms, which are terms that have the same variable and exponent. Here, 3c3c and −2c-2c are like terms because they both contain the variable cc. Adding or subtracting them gives the net effect of these terms, which in this case is cc. The constants 55 and −17-17 are combined in the same way. By combining all like terms, the original expression simplifies to c−12c – 12, which is the most concise form of the original expression.