Q
QuestionMathematics

Rewrite the expression 12x+ 8 to find an equivalent expression. Show three possible equivalent expressions. What do the rewritten expressions tell you about the relationships among the quantities?

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Answer

Full Solution Locked

Step 1:
: Given the expression 12x + 8, we can factor out a common factor of 4 to simplify the expression.

12x + 8 = 4 \times (3x + 2)

Step 2:
: Now, let's find another equivalent expression by dividing the original expression by 4.

\frac{12x + 8}{4} = 3x + 2

Step 3:
: Lastly, we can rewrite the expression by making the substitution x' = x + 2 / 3.

12(x + \frac{2}{3}) + 8 = 12x + 8 + 8 = 12x + 16

This will give us an expression in terms of x'.

Final Answer

The three equivalent expressions are: \begin{align*} 4 \times (3x + 2) \ 3x + 2 \ 12x + 16 \end{align*} These equivalent expressions illustrate the relationships among the quantities. The first expression, 4 × (3x + 2), shows that the original expression is four times the sum of 3x and 2. The second expression, 3x + 2, demonstrates that the expression can be written as the sum of 3x and 2. The third expression, 12x + 16, highlights that the expression is equivalent to 12 times x plus 16. Overall, these equivalent expressions help us understand the structure and composition of the original expression.

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Q
QuestionMathematics

Answer

Full Solution Locked

Step 1:
: Given the expression 12x + 8, we can factor out a common factor of 4 to simplify the expression.

Step 2:
: Now, let's find another equivalent expression by dividing the original expression by 4.

Step 3:
: Lastly, we can rewrite the expression by making the substitution x' = x + 2 / 3.

Final Answer

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QQuestionMathematics

AnswerHelpful

Full Solution Locked

Step 1:: Given the expression 12x + 8, we can factor out a common factor of 4 to simplify the expression.

Step 2:: Now, let's find another equivalent expression by dividing the original expression by 4.

Step 3:: Lastly, we can rewrite the expression by making the substitution x' = x + 2 / 3.

Final Answer

Need Help with Homework?

Related Questions

Q
QuestionMathematics

Answer

Step 1:
: Given the expression 12x + 8, we can factor out a common factor of 4 to simplify the expression.

Step 2:
: Now, let's find another equivalent expression by dividing the original expression by 4.

Step 3:
: Lastly, we can rewrite the expression by making the substitution x' = x + 2 / 3.