To solve the inequality \( \frac{4x}{3} < 4 \), let's first isolate \( x \).
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Multiply both sides by 3 to eliminate the fraction: \[ 4x < 12 \]
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Now, divide both sides by 4: \[ x < 3 \]
So, \( x \) must be less than 3.
Now, your statement "I know this because the fraction I made is ???? 1." suggests that you might be referring to some condition involving a fraction that evaluates to a value related to 1.
Given that:
- If \( x < 3 \), then \( \frac{4x}{3} < 4 \) holds true.
- If \( x = 3 \), then \( \frac{4x}{3} = 4 \).
- If \( x > 3 \), then \( \frac{4x}{3} > 4 \).
In this case, when we plug in different values for \( x \):
- For \( x = 2 \): \( \frac{4(2)}{3} = \frac{8}{3} \) which is approximately 2.67 (less than 4).
- For \( x = 3 \): \( \frac{4(3)}{3} = \frac{12}{3} = 4 \) (equal to 4).
- For \( x = 4 \): \( \frac{4(4)}{3} = \frac{16}{3} \) which is approximately 5.33 (greater than 4).
So, you could fill in the blank with "less than" (for x < 3), "equal to" (for x = 3), or "greater than" (for x > 3) to describe the relationship of \( \frac{4x}{3} \) with respect to 4, depending on the value of \( x \).
If you mean to describe all values that \( 4x/3 \) can take for all values of \( x \) in the context of the inequality being less than 4, then the correct completion of your sentence is "less than".