A poll estimates that 43% of likely voters are in favor of additional restrictions on teenage drivers. The poll has a margin of error of plus or minus 4%. Write and solve an absolute value equation to find the minimum and maximum percent of voters that actually support the restrictions.
with V voters, poll returns .43 as an answer. So, using R as the real value,
|R-.43| <= 0.04R
To find the minimum and maximum percent of voters that actually support the restrictions, we need to consider the margin of error around the estimated percentage of 43%.
Let's denote the minimum percent as "x" and the maximum percent as "y."
According to the given information, the minimum value would be 43% minus the margin of error of 4%, which gives us x = 43% - 4% = 39%.
The maximum value would be 43% plus the margin of error of 4%, which gives us y = 43% + 4% = 47%.
Therefore, the minimum percent of voters that actually support the restrictions is 39%, and the maximum percent is 47%.
To find the minimum and maximum percent of voters that actually support the restrictions, we need to consider the margin of error for the poll.
Let's assume the true percentage of voters in favor of additional restrictions is represented by the variable "x."
The minimum percentage of voters in favor of additional restrictions would be x minus the margin of error, which is 4%. Therefore, the minimum percentage can be expressed as (x - 0.04).
Similarly, the maximum percentage of voters in favor of additional restrictions would be x plus the margin of error, which is 4%. Therefore, the maximum percentage can be expressed as (x + 0.04).
To find the values of x (the true percentage of voters in favor of additional restrictions), we can write the following absolute value equation:
|x - 0.43 | = 0.04
The equation represents the difference between the assumed true percentage and the reported percentage (43%). The absolute value is used to negate the negative value (under the assumption of people not being less than 43%) and ensure we consider any positive difference either side of 43%.
To solve the equation, we can split it into two cases based on the positive and negative values within the absolute value:
Case 1: x - 0.43 = 0.04
Solving for x:
x = 0.04 + 0.43
x = 0.47
Case 2: -(x - 0.43) = 0.04 (negating the negative value)
Solving for x:
-x + 0.43 = 0.04
-x = -0.39
x = 0.39
Therefore, the minimum percentage of voters in favor of additional restrictions is 39% (0.39) while the maximum percentage is 47% (0.47).