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What steps should be followed in order to solve the inequality statement?

n/7 -8 < -11

add 8, divide by 7, and keep the inequality symbol
add 8, multiply by 7, and flip the inequality symbol
add 8, multiply by 7, and keep the inequality symbol
add 8, divide by 7, and flip the inequality symbol

1 answer

To solve the inequality statement \( \frac{n}{7} - 8 < -11 \), follow these steps:

  1. Add 8 to both sides: This simplifies the inequality.

    \[ \frac{n}{7} - 8 + 8 < -11 + 8 \] Which simplifies to: \[ \frac{n}{7} < -3 \]

  2. Multiply both sides by 7: Since 7 is a positive number, the direction of the inequality remains the same.

    \[ 7 \cdot \frac{n}{7} < -3 \cdot 7 \] This simplifies to: \[ n < -21 \]

Thus, the correct sequence of steps involves adding 8, multiplying by 7, and keeping the inequality symbol.

So the correct answer is:

  • add 8, multiply by 7, and keep the inequality symbol.