Solve Two-Step Inequalities Quick Check 1 of 51 of 5 Items Question Solve 8x+4≥52.(1 point) Responses x≥7 x greater than or equal to 7 x≥6 x greater than or equal to 6 x≥2.5 x greater than or equal to 2.5 x≥11
To solve the inequality 8x + 4 ≥ 52, we need to get x by itself on one side of the inequality.
First, subtract 4 from both sides of the inequality:
8x + 4 - 4 ≥ 52 - 4
8x ≥ 48
Next, divide both sides of the inequality by 8:
8x/8 ≥ 48/8
x ≥ 6
So, the correct response is: x ≥ 6
Solve Two-Step Inequalities Quick Check 2 of 52 of 5 Items Question Solve 14x−34>514.(1 point) Responses x>24 x greater than 24 x>2134 x greater than 21 Start Fraction 3 over 4 end fraction x>18 x greater than 18 x>112
To solve the inequality 14x - 34 > 514, we need to get x by itself on one side of the inequality.
First, add 34 to both sides of the inequality:
14x - 34 + 34 > 514 + 34
14x > 548
Next, divide both sides of the inequality by 14:
14x/14 > 548/14
x > 39.14
So, the correct response is: x > 39.14
Solve Two-Step Inequalities Quick Check 2 of 52 of 5 Items Question Solve 1/4x − 3/4>5 1/4.(1 point) Responses x>24 x greater than 24 x>2134 x greater than 21 Start Fraction 3 over 4 end fraction x>18 x greater than 18 x>112
To solve the inequality 1/4x - 3/4 > 5 1/4, we need to get x by itself on one side of the inequality.
First, add 3/4 to both sides of the inequality:
1/4x - 3/4 + 3/4 > 5 1/4 + 3/4
1/4x > 5 5/4
Next, multiply both sides of the inequality by 4 to eliminate the fraction:
4 * (1/4x) > 4 * (5 5/4)
x > 21
So, the correct response is: x > 21
Solve Two-Step Inequalities Quick Check 3 of 53 of 5 Items Question Solve the inequality 6x+9>57. Which of the following graphs shows the solution?(1 point) Responses Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18. Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2. Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2. Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18. Skip to navigation
To solve the inequality 6x + 9 > 57, we need to isolate x.
First, subtract 9 from both sides of the inequality:
6x + 9 - 9 > 57 - 9
6x > 48
Next, divide both sides of the inequality by 6:
6x/6 > 48/6
x > 8
The solution to the inequality is x > 8, which means x is greater than 8.
From the given responses:
Image A: The open point is plotted at 11 and a rightward arrow extends beyond 18. This does not show the solution, as it includes numbers greater than the solution.
Image B: The open point is plotted at 8 and a leftward arrow extends beyond negative 2. This does not show the solution, as it includes numbers less than the solution.
Image C: The open point is plotted at 11 and a leftward arrow extends beyond negative 2. This does not show the solution, as it includes numbers less than the solution.
Image D: The open point is plotted at 8 and a rightward arrow extends beyond 18. This correctly shows the solution, as it only includes numbers greater than 8.
Therefore, the correct response is the image with the rightward arrow on the number line starting at the open point plotted at 8.
Solve Two-Step Inequalities Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Hessa solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve? (1 point) Responses 35x+25≥325 Start Fraction 3 over 5 end fraction x plus Start Fraction 2 over 5 end fraction greater than or equal to 3 Start Fraction 2 over 5 end fraction 25x−45≥115 Start Fraction 2 over 5 end fraction x minus Start Fraction 4 over 5 end fraction greater than or equal to 1 Start Fraction 1 over 5 end fraction 15x−35≤25 Start Fraction 1 over 5 end fraction x minus Start Fraction 3 over 5 end fraction less than or equal to Start Fraction 2 over 5 end fraction 37x+17≤167
Based on the given image, the open point on the number line is plotted at 1, with a rightward arrow extending to the right. This indicates that the solution includes numbers greater than 1.
Looking at the given response options:
Option A: 35x + 25 ≥ 325 does not match the graphed solution because it does not include a "greater than" or "less than" inequality symbol.
Option B: (3/5)x + (2/5) ≥ 3 does not match the graphed solution because it includes a "greater than or equal to" inequality symbol, while the graph shows a "greater than" symbol.
Option C: 25x - 45 ≥ 115 does not match the graphed solution because it does not include a "greater than" or "less than" inequality symbol.
Option D: (2/5)x - (4/5) ≥ 1 matches the graphed solution, as it includes a "greater than" inequality symbol and the open point on the number line is plotted at 1.
Option E: 15x - 35 ≤ 25 does not match the graphed solution because it does not include a "greater than" inequality symbol.
Therefore, the correct response is the inequality (2/5)x - (4/5) ≥ 1.