Hessa solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
(1 point)
1/5x-3/5<2/5
3/5x+2/5>3 2/5
2/5x-4/5>1 1/5
3/7x+1/7<1 6/7
The inequality that Hessa solved is 2/5x - 4/5 > 1 1/5.
Solve the inequality 9.5x - 1.25 < 32.
To solve the inequality 9.5x - 1.25 < 32, we can start by isolating the variable x.
Adding 1.25 to both sides of the inequality, we get:
9.5x - 1.25 + 1.25 < 32 + 1.25
9.5x < 33.25
Next, to solve for x, we divide both sides of the inequality by 9.5:
(9.5x)/9.5 < 33.25/9.5
x < 3.5
So the solution to the inequality is x < 3.5.
To determine which inequality Hessa solved, we need to analyze each option provided and see which one matches the given information.
Let's start by examining the options one by one:
Option 1: 1/5x - 3/5 < 2/5
Option 2: 3/5x + 2/5 > 3 2/5
Option 3: 2/5x - 4/5 > 1 1/5
Option 4: 3/7x + 1/7 < 1 6/7
Hessa solved the inequality and graphed the solution on the number line. By looking at the options, we can determine the inequalities that represent solutions graphed on the number line.
Let's analyze each option based on the given information:
Option 1: 1/5x - 3/5 < 2/5
In this option, the inequality is a "less than" symbol. When this type of inequality is solved and graphed on the number line, the solution appears shaded to the left of the endpoint.
Option 2: 3/5x + 2/5 > 3 2/5
In this option, the inequality is a "greater than" symbol. When this type of inequality is solved and graphed on the number line, the solution appears shaded to the right of the endpoint.
Option 3: 2/5x - 4/5 > 1 1/5
Similar to option 2, this inequality is a "greater than" symbol. The solution would be shaded to the right of the endpoint on the number line.
Option 4: 3/7x + 1/7 < 1 6/7
In this option, the inequality is a "less than" symbol. When this type of inequality is solved and graphed on the number line, the solution appears shaded to the left of the endpoint.
Based on the analysis, only option 1 matches the given information. Therefore, Hessa solved the inequality 1/5x - 3/5 < 2/5.