Use the image to answer the question.
A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 4. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.
Paolo solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(1 point)
Responses
4.9x>19.6
4.9 x greater than 19.6
3.7x>14.8
3.7 x greater than 14.8
2.8x<10.5
2.8 x less than 10.5
2.1x<8.4
2.1 x less than 8.4
Solve 8x−14≤10. Make sure to write your inequality so that x comes first.(1 point)
8x - 14 ≤ 10
solve it
To solve the inequality 8x - 14 ≤ 10, we need to isolate the variable x.
First, we can add 14 to both sides of the inequality:
8x - 14 + 14 ≤ 10 + 14
This simplifies to:
8x ≤ 24
Next, we divide both sides of the inequality by 8 to solve for x:
8x/8 ≤ 24/8
This further simplifies to:
x ≤ 3
Therefore, the solution to the inequality is x ≤ 3.
Solve 5.14x + 2.25 > 15.1. Write the rational number in your answer in decimal form to the tenths place. Make sure to write your inequality so that x comes first. (1 point)
To solve the inequality 5.14x + 2.25 > 15.1, we start by isolating the variable x.
First, we can subtract 2.25 from both sides of the inequality:
5.14x + 2.25 - 2.25 > 15.1 - 2.25
This simplifies to:
5.14x > 12.85
Next, we divide both sides of the inequality by 5.14 to solve for x:
5.14x/5.14 > 12.85/5.14
This further simplifies to:
x > 2.50
Therefore, the solution to the inequality is x > 2.5.
Use the image to answer the question.
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 1 and 2. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(1 point)
Responses
3.4x−1.2≥4.75
3.4 x minus 1.2 greater than or equal to 4.75
0.9x+2.8≤5.95
0.9 x plus 2.8 less than or equal to 5.95
5.6x−18.9≤0.7
5.6 x minus 18.9 less than or equal to 0.7
2.1x+5.6≥8.75