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What are some challenging Algebra I questions and answers?

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The more challenging Algebra 1 problems are quadratic equations of the form ax^2 +bx +c =0, where the general solution is given by the quadratic formula: x = (-b +/- sqrt(b^2-4ac))/2a (where sqrt means a square root of the term in parentheses). For example, if the equation is 2x^2 +2x - 4= 0, the solution is given by (-2 +/- sqrt(2^2 - 4*2*(-4))/(2*2) = (-2 +/- sqrt(4+32))/4 = (-2 +/- sqrt(36))/4 = (-2+6)/4 =1 or = (-2-6)/4=-2.

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The example question can also be solved by factoring. If the equation is divided by 2, making it x^2 +x-2=0, the equation factors to (x-1)(x+2) =0, which again becomes x =1 or x = -2.

Another type of problem that often challenges Algebra I students is word problems, such as rate-time-distance problems, age problems, interest rate problems, number problems and price problems. An example of a price problem is: Wilma spends $42 on a pair of shoes, which is $14 less than twice what she spent on stockings. How much were the stockings? The solution is to let the price of stockings = x, then 42=2x - 14. 42+14 = 2x = 56, and x = $28 for the stockings.

An example of a number problem is: The sum of two consecutive integers is 47. What are the numbers? The solution is based on the fact that the two numbers can be represented as x and (x+1). Then x+(x+1) = 2x+1 = 47, or 2x =46. This means x = 23 and x + 1 is 24.

Other example word problems can be found online, sometimes with solutions. If solutions are not readily available, an online math tutor or walk-in tutoring can help.

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