Math Problem Statement

Evaluate the expression below when a = 3, b = 4, and c = 1. What is the value of 3x - (-2) when x = 6? Simplify the expression -4(2x + 2) - 9x.

Solution

Let's break down the questions on the image:

Question 3:

You are asked to evaluate the expression below when a=3a = 3, b=4b = 4, and c=1c = 1.

Expression: c+4b+ac + 4b + a

To solve this:

  • Substitute the values of a=3a = 3, b=4b = 4, and c=1c = 1 into the expression.

c+4b+a=1+4(4)+3c + 4b + a = 1 + 4(4) + 3

Now calculate:

1+16+3=201 + 16 + 3 = 20

So, the value of the expression is 20.


Question 4:

You are asked to find the value of 3x(2)3x - (-2) when x=6x = 6.

This simplifies to:

3(6)(2)=18+2=203(6) - (-2) = 18 + 2 = 20

So, the value is 20.


Question 5:

The expression you need to simplify is:

4(2x+2)9x-4(2x + 2) - 9x

Distribute the -4:

4(2x)4(2)9x=8x89x-4(2x) - 4(2) - 9x = -8x - 8 - 9x

Now, combine like terms:

8x9x8=17x8-8x - 9x - 8 = -17x - 8

So, the simplified expression is 17x8\boxed{-17x - 8}.


Would you like to explore any of these problems further or have any questions?

Related Questions:

  1. What happens if a=5a = 5 and b=2b = 2 in the first expression?
  2. How does the result change if x=6x = -6 in the second problem?
  3. What other methods can be used to simplify expressions like the one in question 5?
  4. How do we solve for a variable if we are given a value for the expression instead of the variable itself?
  5. What is the importance of distributing terms in algebraic expressions?

Tip: Always check if you can combine like terms before simplifying, as this reduces the complexity of the expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Expression Evaluation
Simplification of Algebraic Expressions

Formulas

c + 4b + a
3x - (-2)
-4(2x + 2) - 9x

Theorems

Distributive Property

Suitable Grade Level

Grades 6-8