Substituting Values in Algebraic Expressions

Oct 13, 2025 by thesweetdesigns.com 23 views

Understanding Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving equations and inequalities. An algebraic expression is a combination of variables, constants, and mathematical operations. When evaluating an algebraic expression, we need to substitute the given value for the variable and simplify the expression.

Substituting Values in Algebraic Expressions

When evaluating an algebraic expression, we need to substitute the given value for the variable. The variable is the part of the expression that contains the letter or symbol that represents the unknown value. In the given expression, ${$ (6x + 9)^2 - 5$}$, the variable is ${$ x$}$.

Evaluating the Expression

To evaluate the expression, we need to substitute the given value for the variable. In this case, the given value is ${$ x = 1$}$. We need to substitute ${$ x = 1$}$ for the variable ${$ x$}$ in the expression.

Substituting ${$ x = 1$}$ for the Variable ${$ x$}$

When we substitute ${$ x = 1$}$ for the variable ${$ x$}$, the expression becomes:

${$ (6(1) + 9)^2 - 5$}$

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

Evaluate the expression inside the parentheses: ${ $6(1) + 9\$}$
Simplify the expression: ${ $6 + 9 = 15\$}$
Raise 15 to the power of 2: ${ $15^2 = 225\$}$
Subtract 5 from 225: ${ $225 - 5 = 220\$}$

Final Answer

Therefore, when evaluating the expression ${$ (6x + 9)^2 - 5$}$ for ${$ x = 1$}$, the given value of 1 is substituted for the variable ${$ x$}$.

Conclusion

In conclusion, when evaluating an algebraic expression, we need to substitute the given value for the variable. The variable is the part of the expression that contains the letter or symbol that represents the unknown value. In the given expression, ${$ (6x + 9)^2 - 5$}$, the variable is ${$ x$}$. We need to substitute ${$ x = 1$}$ for the variable ${$ x$}$ in the expression and simplify the expression to get the final answer.

Frequently Asked Questions

Q: What is an algebraic expression?

A: An algebraic expression is a combination of variables, constants, and mathematical operations.

Q: What is the variable in the expression ${$ (6x + 9)^2 - 5$}$?

A: The variable in the expression ${$ (6x + 9)^2 - 5$}$ is ${$ x$}$.

Q: What is the given value in the expression ${$ (6x + 9)^2 - 5$}$?

A: The given value in the expression ${$ (6x + 9)^2 - 5$}$ is ${$ x = 1$}$.

Q: What is the final answer when evaluating the expression ${$ (6x + 9)^2 - 5$}$ for ${$ x = 1$}$?

Understanding Algebraic Expressions

Substituting Values in Algebraic Expressions

Evaluating the Expression

Substituting ${$ x = 1$}$ for the Variable ${$ x$}$

When we substitute ${$ x = 1$}$ for the variable ${$ x$}$, the expression becomes: