Question
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Tutor-Verified Answer
Answer
The solution is \( y > 4 \) or \( y < 1 \).
Solution
### Solving \( 16 y-18>46 \) OR \( 14 y+6<20 \)
#### First Inequality: \( 16y - 18 > 46 \)
1. **Add 18 to both sides:**
\[
16y - 18 + 18 > 46 + 18
\]
Simplifies to:
\[
16y > 64
\]
2. **Divide both sides by 16:**
\[
y > \frac{64}{16}
\]
Thus:
\[
y > 4
\]
#### Second Inequality: \( 14y + 6 < 20 \)
1. **Subtract 6 from both sides:**
\[
14y + 6 - 6 < 20 - 6
\]
Simplifies to:
\[
14y < 14
\]
2. **Divide both sides by 14:**
\[
y < \frac{14}{14}
\]
Thus:
\[
y < 1
\]
### Final Answer
The solution to the inequality is:
\[
y > 4 \quad \text{or} \quad y < 1
\]
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Simplify this solution Beyond the Answer
To solve the first inequality \( 16y - 18 > 46 \), add 18 to both sides to get \( 16y > 64 \). Then divide both sides by 16, yielding \( y > 4 \). For the second inequality \( 14y + 6 < 20 \), subtract 6 from both sides to find \( 14y < 14 \). Dividing both sides by 14 gives \( y < 1 \). Therefore, the solution is \( y > 4 \) OR \( y < 1 \). This means any value of \( y \) that is greater than 4 or less than 1 will satisfy at least one of the inequalities! Now, time to get those values and make those inequalities work for you!
