absolute value equation in percentages - know answer but can't write out equation & steps to solve

Question

according to a poll for an upcoming school board election 40% of voters are likely to vote for the incumbent. the poll shows a margin of error of +3 or -3 percentage points. write and solve and absolute value equation to find the least and the greatest presents of voters v likely to vote for the incumbent

Answer 1

Let v represent the percentage of voters for the incumbent.

 

The difference between this v and 40% represents the margin of error and the margin of error is ±3.

 

Then |v - 40| = |±3| = 3.

 

To solve for the percentage, this represents two equations, one for error 3 and one for error -3.

 

For the error 3,  v - 40 = 3 and v = 43 or 43%

For the error -3, v - 40 = -3 and v = 37 or 37%

 

The incumbent is expected to win between 37% and 43% of the voters