Question 1119374: The Johnson Family is looking to buy a new house on Belmont Road. Their insurance deductible is increased by $500 if they live more than 2 miles away from the fire department. (a) Write an absolute value inequality that represents the distance from the fire department that will be the best location on Belmont Road for the Johnson's to buy their home if they don't want to pay the increased deductible. The location of the fire department is at 0 miles with Belmont Road extending another 10 miles in each direction. (b) Solve the inequality.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they have to live within plus or minus 2 miles from the firehouse.
the absolute value equation will be abs(0 + x) < 2, where x represents the distance from the firehouse and mile marker 0 represents the location of the firehouse.
abs(0 + x) < 2 is equal to (0 + x) < 2 when 0 + x is positive and -(0 + x) < 2 when 0 + x is negative.
0 + x is the expression within the absolute value sign.
when 0 + x is positive, the inequality is (0 + x) < 2.
solve for x to get x < 2.
when 0 + x is negative, the inequality is - (0 + x) < 2.
solve for x to get -x < 2 which results in x > -2.
your answer is -2 < x < 2, which means the house must be within plus or minus 2 miles from the location of the firehouse, which is at location 0.
the house has to be between mile marker -2 and mile marker 2 on belmont road.
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