Solve Two-Step Inequalities Quick Check
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Question
Solve the inequality 9.5x−1.25<32 . Which of the following graphs shows the solution?(1 point)
Responses
A. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
B. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
C. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
D. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
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The correct graph that shows the solution to the inequality 9.5x - 1.25 < 32 is option C.
In option C, an open point is plotted on the number line between 3 and 4, just after 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10. This represents all the values of x that satisfy the inequality.
Recheck
Apologies for the mistake. Let's recheck the options.
The inequality we have is 9.5x - 1.25 < 32.
To solve it, we can start by isolating the variable x. Adding 1.25 to both sides of the inequality, we get:
9.5x < 33.25.
Next, we divide both sides of the inequality by 9.5 to solve for x:
x < 33.25/9.5.
Simplifying, we have:
x < 3.5.
Now, let's consider the given options again:
A. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
B. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
C. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
D. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Based on our solution x < 3.5, option C is the correct graph.
Are you sure
You are right, I apologize for the confusion. My previous response was incorrect.
Let's recheck the options and solve the inequality again.
The inequality is 9.5x - 1.25 < 32.
To solve it, we can start by isolating the variable x. Adding 1.25 to both sides of the inequality, we get:
9.5x < 33.25.
Next, divide both sides of the inequality by 9.5:
x < 33.25/9.5.
Simplifying, we have:
x < 3.5.
Now let's consider the given options:
A. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
B. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
C. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
D. A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Based on our solution x < 3.5, the correct graph that shows the solution is option A.
In option A, an open point is plotted on the number line between 3 and 4, and a leftward arrow originates at the open point and goes beyond negative 10. This represents all the values of x that satisfy the inequality.