Тема: Problem Solving Algebra 1?

Welcome to Algebra 1. This course will make math come alive with its many intriguing examples of algebra in the world around you, from baseball to theater lighting to.

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Продолжая тему обмена опытом жизни за границей, я взяла интервью у Полины Ермолаевой. В этом выпуске она расскажет о том, как ей удалось выиграть грант на образование в США, и что ей дала эта учеба.

P.S. Девушка далеко не так наивна и наигранна, как может показаться:)

Problem 1: Combine elements with the same powers as follows by distributing the minus sign: (3x^2 - x^2) + (-4x - 5x) + (-5 - -6) = 2x^2 -9x+1 Problem 2: The x-intercept is when y=0. In this case, y=x^2+2x-8=0. Factor the equation: (x+4)(x-2)=0 Therefore, the x-intercepts occur at -4 and 2

Here s how you do this. Think of these equations as tangled up string. In order to untangle them, you have to reverse the process that got them tangled up in the first place. You probably know the order of operations (powers & roots, multiplication & division, addition & subtraction), so when you untangle equations, do so in the opposite order of operations (addition & subtraction first, followed by multiplication & division, followed by powers & roots). For these equations you want to get all of the x s on one side and the plain numbers on the other. Start with addition & subtraction. Isolate the √x term on one side by using addition & subtraction: √x + 7 = x - 5 To move the 7 to the other side, undo what s being done. Since the 7 is added to the √x, then do the opposite of adding. Subtract 7 from both sides: √x + 7 - 7 = x - 5 - 7 Now add up like terms (numbers only together and x terms together) √x + 0 = x - 12 √x = x - 12 Now square both sides to do the opposite of the √ (√x)² = (x - 12)² x = x² - 24x + 144 Now subtract x from both sides to set up a quadratic solution: 0 = x² - 25x + 144 Now try to figure out how this can be factored. You have to find 2 factors of 144 that when you add them they will be 25. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144. I m going to guess 9 might work. 144 ÷ 9 = 16 or 9 x 16 = 144, also 9 + 16 = 25. We have a winner! So the factors of that equation are: (x - 9) (x - 16) Then the equation can be changed to: 0 = (x - 9) (x - 16) Set each factor equal to zero: 0 = (x - 9) and 0 = (x - 16) The solutions are x = 9 and x = 16 x - 9 = √x - 3 This one will be a bit easier: Isolate the √x by undoing what is done to it: undo the - 3 by adding 3 to both sides: x - 9 + 3 = √x - 3 + 3 x - 6 = √x Undo the √x by squaring both sides: (x - 6)² = x x² - 12x + 36 = x Subtract x from both sides: x² - 12x - x + 36 = x - x x² - 13x + 36 = 0 Now what are the factors of 36? Find 2 that will add up to 13. Simple (9 x 4) = 36 and 9 + 4 = 13 (x - 9) (x - 4) = 0 x = 9 and x = 4 For the 3rd and 4th problems, I m not sure whether the x is supposed to be under or just next to the radical. But it s late and I am going to bed now. Do the last 2 problems the same way: isolate the radical and square both sides. If the x is supposed to be under the radical, then square it too, otherwise, divide both sides by x before you square both sides. That would make things a bit messy, so my guess is that the x is probably supposed to be under the radical too. No biggie. √2x + 3 = 6 - x subtract 3 from both sides: √2x + 3 - 3 = 6 - 3 - x √2x = 3 - x (√2x)² = (3 - x)² 2x = 9 - 6x + x² Move everything to one side: 2x - 2x = 9 - 6x - 2x + x² 0 = x² - 8x + 9 This one will take the dreaded quadratic formula to complete. Good night & good luck.

1) 18 - 4k = 1 - 4k.......................... Add 4K ... 18 = 10............................ FALSE The statement is false, therefore NO SOLUTION The others are correct. ( see above )

Home » Inequalities Solving and Graphing Inequalities. If you are beginning your study of inequalities, I have a lot of lessons for you to study.

The Art of Problem Solving texts have been used by tens of thousands of outstanding students, including many winners of major national contests such as MATHCOUNTS and the American Mathematics Competitions.

This course will make math come alive with its many intriguing examples of algebra in the world around you, from baseball to theater lighting to space exploration. Need a little extra help? Want a problem solving challenge? Click on the chapter links below to get lesson help, try an extra challenge, or explore application and career links.