algebra i is a course designed to give students a firm understanding of mathematical equations that involve variables, as well as to teach them the basics of graphing and manipulating simple functions. a major part of algebra i is learning to convert information from equations to graphs and from graphs to equations, and understanding how to analyze equations and graphs as related concepts is a core part of the course. inequalities are also taught in algebra i in the same manner as equations—that is, with an emphasis on representing them on number lines or graphing them. the mathematical concepts that students master in algebra i form the core of their mathematical understanding in many later classes in math and the sciences.

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solving for the variable, x, gives xp = 5, where x=5/p. sally can paint 1/4 of the house in 1 hour. in order to determine how long it will take them to paint the house, when working together, the following equation may be written: 1/4 x+1/6 x=1. in order to solve for a, both sides of the equation may first be multiplied by 3. this is written as 3(2a/3)=3(8+4a) or 2a=24+12a. division by -10 gives a = -2.4. three equations may initially be written to represent the given information. since the sum of the three ages is 41, we may write, l + s + j = 41, where l represents leah’s age, s represents sue’s age, and j represents john’s age. simple interest is represented by the formula, i = prt, where p represents the principal amount, r represents the interest rate, and t represents the time. substituting $4,000 for p, 0.06 for r, and 5 for t gives i = (4000)(0.06)(5), or i = 1,200. so, he will receive $1,200 in interest.

the sum of $80 and $93.75 is $173.75, so he was paid $173.75 for 14.25 hours of work. if she removes only 12 jellybeans, green or blue may not be represented. the value of z may be determined by dividing both sides of the equation, r=5z, by 5. doing so gives r/5=z. 50 cents is half of one dollar, thus the ratio is written as half of 300, or 150, to x. the equation representing this situation is 300/x*1/2=150/x. the following proportion may be used to determine how much lee will make next week: 22/132=15/x. the given equation should be solved for x. doing so gives x = 6. substituting the x-value of 6 into the expression, 5x + 3, gives 5(6) + 3, or 33. the amount you will pay for the book may be represented by the expression, 80+(80*0.0825). the change you will receive is equal to the difference of $100 and $86.60, or $13.40. thus, the total cost may be represented by the expression, 40(2.35) + 3(12.95).

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