You randomly survey students about year-round school. The results are shown in the graph.

A bar graph shows the percent of students who favor or oppose year-round school. The percent who oppose is 68 percent. The percent who favor is 32 percent. The error is plus or minus 5 percent.

The error given in the graph means that the actual percent could be 5% more or 5% less than the percent reported by the survey.

a. Write and solve an absolute value equation to find the least and greatest percentages of students who could be in favor of year-round school. Use $x$ as the variable in the equation.

27% and 37%

Step-by-step explanation:

Percentage of students who oppose the year-round school = 68%

Percentage of students who support the year-round school = 32%

Margin of error = ± 5%

We have to set up the absolute valued equation to find the range (least and greatest) percentages of students who could be in favor of year-round school.

Since, the percentage of students who support the year-round school is 32% and the margin of error is 5%, this means, the difference between 32% and the least and greatest possible percentages is 5%. It can be either + 5% or - 5%

This thing can be expressed as absolute valued equation as:

| x - 32 | = 5

Here x represents the least and greatest percentages.

Expanding the equation, we can write:

x - 32 = - 5 or x - 32 = 5

x = - 5 + 32 or x = 5 + 32

x = 27% x = 37%

This means the least percentage of students who be in favor is 27% and the greatest percentage of students is 37%.