Question
\( x=3 y-4 \) If \( x=3 \), which of the following statements is not true? \( y>2 \)
Ask by Carter Hampton. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When \( x = 3 \), \( y = \frac{7}{3} \), which is approximately 2.33. Since 2.33 is greater than 2, the statement \( y > 2 \) is true. Therefore, there is no statement provided that is not true based on the given conditions.
Solution
To determine which statement is not true, we first need to substitute \( x = 3 \) into the equation \( x = 3y - 4 \) and solve for \( y \).
1. Substitute \( x = 3 \) into the equation:
\[
3 = 3y - 4
\]
2. Add 4 to both sides:
\[
3 + 4 = 3y
\]
\[
7 = 3y
\]
3. Divide both sides by 3 to solve for \( y \):
\[
y = \frac{7}{3}
\]
Now, we need to evaluate the statement \( y > 2 \).
4. Calculate \( \frac{7}{3} \):
\[
\frac{7}{3} \approx 2.33
\]
Since \( 2.33 > 2 \), the statement \( y > 2 \) is true.
Thus, the statement that is not true is that \( y > 2 \) is false.
In conclusion, the statement \( y > 2 \) is true, so there is no statement provided that is not true based on the given conditions.
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Simplify this solution The Deep Dive
Let's plug in \( x=3 \) into the equation \( x=3y-4 \): \[ 3 = 3y - 4 \] Now, solving for \( y \), we first add 4 to both sides: \[ 3 + 4 = 3y \] \[ 7 = 3y \] Next, divide both sides by 3: \[ y = \frac{7}{3} \approx 2.33 \] Since \( \frac{7}{3} \) is indeed greater than 2, the statement \( y > 2 \) is true. Hence, \( y > 2 \) is not the statement that is not true. In this case, if there's a statement claiming anything different about \( y \) being less than or equal to 2, that would be the false one!
