Solve the inequality 2/3x≤5 . Which of the following graphs shows the solution? (1 point)
Responses thanks
A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
11 answers
A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 2/3. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
First, we can multiply both sides of the inequality by 3 to eliminate the fraction:
(2/3)x * 3 ≤ 5 * 3
This simplifies to:
2x ≤ 15
Next, we divide both sides by 2 to solve for x:
(2x) / 2 ≤ 15 / 2
This simplifies to:
x ≤ 7.5
So the solution to the inequality is x ≤ 7.5.
The graph that represents this solution correctly is the second option, where a closed point is plotted on the number line at 5 2/3 (which is equivalent to 7.5), and a leftward arrow is marked on the number line originating from that closed point and going beyond negative 10.