7. Winona and her mom buy ribbon to wrap presents. The cost of $$ p $$ inches of plain ribbon is represented by $$ 6 p $$. The cost of $$ p $$ inches of striped ribbon is represented by $$ 6 p+9 $$. Winona says that $$ 6 p=6 p+9 $$ for any value of $$ p $$ because the coefficients of $$ p $$ are the same on both sides of the equation. Is Winona correct? Explain.

Question

UpStudy AI · Accepted Answer

To determine if Winona is correct, we need to analyze the equation she proposed:

$$
6p = 6p + 9
$$

### Step 1: Simplify the Equation

We can start by simplifying the equation. If we subtract $$ 6p $$ from both sides, we get:

$$
6p - 6p = 6p + 9 - 6p
$$

This simplifies to:

$$
0 = 9
$$

### Step 2: Analyze the Result

The equation $$ 0 = 9 $$ is a contradiction. This means that the original equation $$ 6p = 6p + 9 $$ cannot be true for any value of $$ p $$.

### Conclusion

Winona's assertion that $$ 6p = 6p + 9 $$ for any value of $$ p $$ is incorrect. The coefficients of $$ p $$ being the same does not imply that the two expressions are equal; the constant term on the right side (which is $$ 9 $$) makes the two sides unequal. Therefore, the equation is false for all values of $$ p $$.
Winona is not correct. The equation $$6p = 6p + 9$$ simplifies to $$0 = 9$$, which is always false. Therefore, the equation does not hold true for any value of $$p$$.

Winona and her mom buy ribbon to wrap presents. The cost of inches of
plain ribbon is represented by . The cost of inches of striped ribbon is
represented by . Winona says that for any value of
because the coefficients of are the same on both sides of the equation.
Is Winona correct? Explain.

Upstudy AI Solution

Answer

Solution

Step 1: Simplify the Equation

Step 2: Analyze the Result

Conclusion

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Winona and her mom buy ribbon to wrap presents. The cost of inches of plain ribbon is represented by . The cost of inches of striped ribbon is represented by . Winona says that for any value of because the coefficients of are the same on both sides of the equation. Is Winona correct? Explain.