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Solve the inequality 9.5x−1.25<32 witch gragh 1 2 3 or 4 let me lnow

. Which of the following graphs shows the solution?(1 point)
Responses

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.

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.

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.

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.

1 answer

To solve the inequality \( 9.5x - 1.25 < 32 \), we'll first isolate \( x \).

  1. Add \( 1.25 \) to both sides: \[ 9.5x < 32 + 1.25 \] \[ 9.5x < 33.25 \]

  2. Now, divide both sides by \( 9.5 \): \[ x < \frac{33.25}{9.5} \]

Calculating \( \frac{33.25}{9.5} \): \[ x < 3.5 \]

This means that the solution to the inequality is \( x < 3.5 \).

Now, regarding the graphical representation of this solution on a number line:

  • Since the solution is strictly less than \( 3.5 \) (not including \( 3.5 \)), we would use an open point at \( 3.5 \) to indicate that \( 3.5 \) itself is not included.
  • The arrow points to the left from \( 3.5 \) to indicate all values less than \( 3.5 \).

Among the options presented, the correct graph would have an open point just before \( 4 \) (indicating \( 3.5 \)) and a leftward arrow extending indefinitely.

Thus, the correct choice is the second option (an open point is plotted on the number line between 3 and 4, just after the 3, with a leftward arrow).