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Eric is solving the inequality 9x + 15 ≥

51 and graphing the solution. Which of the following describe the steps he should take using inverse operations to solve? (1 point)
Responses

Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.
Divide both sides of the inequality by 9 and then add 15 to both sides of the inequality.

Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.
Subtract 15 from both sides of the inequality and then multiply both sides of the inequality by 9.

Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9 and then subtract 15 from both sides of the inequality.
Question 2
Help Eric draw his answer on the number line by selecting the correct responses below.

(2 points)
Eric would plot the point given in the solution on the number line with a(n)
circle and shade to the
of the point on the number line.

1 answer

To solve the inequality \( 9x + 15 \geq 51 \), we can follow these steps using inverse operations:

  1. Subtract 15 from both sides of the inequality: \[ 9x + 15 - 15 \geq 51 - 15 \implies 9x \geq 36 \]

  2. Divide both sides of the inequality by 9: \[ \frac{9x}{9} \geq \frac{36}{9} \implies x \geq 4 \]

Therefore, the correct response describing the steps Eric should take is: Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

For Question 2:

The solution to the inequality is \( x \geq 4 \).

  • Eric would plot the point given in the solution on the number line with a closed circle since the inequality includes \( 4 \) (due to the "≥" symbol).
  • He would then shade to the right of the point on the number line to represent all numbers greater than or equal to \( 4 \).

So, the correct responses would be: Eric would plot the point given in the solution on the number line with a(n) closed circle and shade to the right of the point on the number line.