Solve x - 2.41 > 4.76(1 point)

Question

Responses

x < 7.17
x < 7.17

x > 2.35
x > 2.35

x < 2.35
x < 2.35

x > 7.17

Use the image to answer the question.

Josie solved an inequality and graphed the solution on the number line. Which or the following inequalities did she solve?

(1 point)
Responses

x - 1.25 ≥
1.25
x - 1.25 is greater than or equal to 1.25

x + 0.5 < 3
x + 0.5 < 3

x - 1.25 ≤
1.25
x - 1.25 is less than or equal to 1.25

x + 1.25 ≥
1.25
x + 1.25 is greater than or equal to 1.25

Solve 1.7x ≥ 5.95
(1 point)
Responses

x ≥
10.115
x is greater than or equal to 10.115

x ≥
7.65
x is greater than or equal to 7.65

x ≥
3.5
x is greater than or equal to 3.5

x ≥
4.25

Solve -5x + 12 < 32(1 point)
Responses

x < -4
x < -4

x < 4
x < 4

x > 4
x > 4

x > -4
x > -4

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 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 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 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 subtract 15 from both sides of the inequality.

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.

Answer 1

Let’s solve each part of your question step-by-step.

1. Solve the inequality \( x - 2.41 > 4.76 \): \[ x - 2.41 > 4.76 \] Add \( 2.41 \) to both sides: \[ x > 4.76 + 2.41 \] \[ x > 7.17 \] Response: \( x > 7.17 \)

2. Josie's inequality: Without the image that describes what Josie’s graph looks like, I can provide guidance on the likely inequalities based on common graph shapes:

   • If the graph shows a closed circle on a point with an arrow to the right, it would correspond to an inequality like \( x \geq k \).
   • If it shows an open circle with arrows to the left, it might reflect an inequality like \( x < k \). Assuming you comprehend the properties of the plotted line:
   • If it's an open circle moving to the left, the answer would be: \( x + 0.5 < 3 \)
   • If it’s a point shaded towards the left at a closed point, it would refer to an equality.

3. Solve \( 1.7x \geq 5.95 \): Divide both sides by \( 1.7 \): \[ x \geq \frac{5.95}{1.7} = 3.5 \] Response: \( x \geq 3.5 \)

4. Solve \( -5x + 12 < 32 \): \[ -5x + 12 < 32 \] Subtract \( 12 \) from both sides: \[ -5x < 20 \] Divide both sides by \( -5 \) (remember to flip the inequality): \[ x > -4 \] Response: \( x > -4 \)

5. Eric's steps to solve \( 9x + 15 \geq 51 \): The correct way to solve for \( x \) is:

   • Subtract \( 15 \) from both sides: \[ 9x \geq 36 \]
   • Then divide by \( 9 \): \[ x \geq 4 \] Response: Subtract 15 from both sides of the inequality and then divide both sides of the inequality by 9.

6. Drawing Eric's answer on the number line:

   • Since \( x \geq 4 \), he's going to put a closed circle on \( 4 \) (because it's inclusive).
   • He will shade to the right of the point on the number line.

   Complete Answer: Eric would plot the point given in the solution on the number line with a closed circle and shade to the right of the point on the number line.

Let me know if you need help with anything else!