course Mth 158 ù‡‚g¸Ïû©¶ø³—®J–öŽå´Eûüq¶Ž³¾¯assignment #010
......!!!!!!!!...................................
13:23:31 query 1.1.20 (was 1.1.12). Explain, step by step, how you solved the equation 5y + 6 = -18 - y
......!!!!!!!!...................................
RESPONSE --> First, I grouped like terms. 5y + y = -18 -y Next, I add like terms. 6y= -24 Last, I divided 24 by 6 so that my y would stand alone. y = -4
.................................................
......!!!!!!!!...................................
13:24:57 ** STUDENT SOLUTION WITH INSTRUCTOR COMMENT: 5y + 6 = 18 - y Subtract 6 from both sides, giving us 5y = 12 - y Add y to both sides, 5y + y = 12 or 6y = 12 divide both sides by 6 y = 2 INSTRUCTOR COMMENT: This is correct for equation 5y + 6 = 18 - y but the equation as I note it is 5y + 6 = -18 - y. If that's the correct equation the solution is found by practically the same steps but you end up with y = -4. **
......!!!!!!!!...................................
RESPONSE --> ok
.................................................
......!!!!!!!!...................................
13:30:08 query 1.1.38 \ 44 (was 1.1.30). Explain, step by step, how you solved the equation (2x+1) / 3 + 16 = 3x
......!!!!!!!!...................................
RESPONSE --> First I got rid of the denominator by multiplying by each side by 3. [(2x + 1)/3 * 3] + 16(3) = 3x(3) (2x+1) + 48 = 9x I then combined like terms. 2x +49 = 9x 49 = 9x - 2x 49= 7x I then divided by 7. 7 = x or x = 7
.................................................
......!!!!!!!!...................................
13:30:16 ** STUDENT SOLUTION: (2x + 1) / 3 + 16 = 3x First, multiply both sides of the equation by 3 2x +1 + 48 =9x or 2x + 49 = 9x subtract 2x from both sides. 49 = 7x Divide both sides by 7 7 = x **
......!!!!!!!!...................................
RESPONSE --> ok
.................................................
......!!!!!!!!...................................
13:37:55 query was 1.1.44 \ 36. Explain, step by step, how you solved the equation (x+2)(x-3) = (x+3)^2
......!!!!!!!!...................................
RESPONSE --> First, I solved for each side like so: x^2 - 3x + 2x -6 = x^2 + 6x + 9 x^2 -x -6 =x^2 + 6x + 9 Then I combined like terms. (x^2 - x^2)+ (-6 - 9) = 6x + x -15 = 7x Then I divided by 7. -15/7 = x
.................................................
......!!!!!!!!...................................
13:38:05 ** STUDENT SOLUTION: (x+2)(x+3) = (x+3)^2 First, we use the distributive property to remove the parenthesis and get x^2 - x - 6 = x^2 + 6x + 9 subtract x^2 from both sides, -x - 6 = 6x + 9 Subtract 9 from both sides - x - 6 - 9 = 6x or -x - 15 = 6x add x to both sides -15 = 7x Divide both sides by 7 -15/7 = x **
......!!!!!!!!...................................
RESPONSE --> ok
.................................................
......!!!!!!!!...................................
13:42:49 query 1.1.52 (was 1.1.48). Explain, step by step, how you solved the equation x / (x^2-9) + 4 / (x+3) = 3 / (x^2-9)/
......!!!!!!!!...................................
RESPONSE --> First I factored the denominators to find the common denominator. x/(x + 3)(x - 3) + 4/(x + 3) = 3/(x + 3)(x - 3) I then mutiplied as needed in the numerators. x + 4(x-3) = 3 x + 4x - 12 = 3 Then I combined like terms and divided by 5. 5x = 15 x = 3
.................................................
......!!!!!!!!...................................
13:44:02 ** Starting with x / (x^2 -9) + 4 / (x+3) = 3 / (x^2 -9), first factor x^2 - 9 to get x / ( (x-3)(x+3) ) + 4 / (x+3) = 3 / ( (x-3)(x+3) ). Multiply both sides by the common denominator ( (x-3)(x+3) ): ( (x-3)(x+3) ) * x / ( (x-3)(x+3) ) + ( (x-3)(x+3) ) * 4 / (x+3) = ( (x-3)(x+3) ) * 3 / ( (x-3)(x+3) ). Simplify: x + 4(x-3) = 3. Simplify x + 4x - 12 = 3 5x = 15 x = 3. If there is a solution to the original equation it is x = 3. However x = 3 results in denominator 0 when substituted into the original equation, and division by 0 is undefined. So there is no solution to the equation. When you multiplied both sides by x-3, if x = 3 you were multiplying by zero, which invalidated your solution **
......!!!!!!!!...................................
RESPONSE --> Trick question.
.................................................
......!!!!!!!!...................................
13:51:16 query 1.1.58 (was 1.1.54). Explain, step by step, how you solved the equation (8w + 5) / (10w - 7) = (4w - 3) / (5w + 7)
......!!!!!!!!...................................
RESPONSE --> I cross multiplied the numerators by the denominators. This is a shortcut, but I believe it works in this situation. (8w + 5)(5w + 7) = (4w - 3)(10w - 7) 40w^2 + 56w + 25w + 35 = 40w^2 - 28w -30w + 21 Then I combined like terms. (40w^2 - 40w^2) +( 81w - 58w) = 21- 35 23w = -14 w= -14/23
.................................................
......!!!!!!!!...................................
13:52:36 ** STUDENT SOLUTION: 1) clear the equation of fractions by multiplying both sides by the LCM (10w - 7)(5W + 7) After cancellation the left side reads: (5w+7)(8w + 5) After cancellation the right side reads: (10w - 7)(4w - 3) multiply the factors on each side using the DISTRIBUTIVE LAW Left side becomes: (40w^2) + 81w + 35 Right side becomes: (40w^2) - 58w + 21 3) subtract 40w^2 from both sides add 58w to both sides subtract 35 from both sides Rewrite: 139w = - 14 Now divide both sides by 139 to get w = - (14 / 139) DER**
......!!!!!!!!...................................
RESPONSE --> I subtracted th 58w instead of adding. Stupid mistake.
.................................................
......!!!!!!!!...................................
13:55:46 query 1.1.70 (was 1.1.78). Explain, step by step, how you solved the equation 1 - a x = b, a <> 0.
......!!!!!!!!...................................
RESPONSE --> First I subtracted 1 from both sides to get -ax = b - 1 Then I divided both sides by -a to get x =( b - 1)/ -a
.................................................
......!!!!!!!!...................................
13:56:49 ** Start with 1 -ax = b, a <> 0. Adding -1 to both sides we get 1 - ax - 1 = b - 1, which we simplify to get -ax = b - 1. Divide both sides by -a, which gives you x = (b - 1) / (-a). Multiply the right-hand side by -1 / -1 to get x = (-b + 1) / a or x = (1 - b) / a. **
......!!!!!!!!...................................
RESPONSE --> ok
.................................................
......!!!!!!!!...................................
14:21:50 query extra problem (was 1.1.72). Explain, step by step, how you solved the equation x^3 + 6 x^2 - 7 x = 0 using factoring.
......!!!!!!!!...................................
RESPONSE --> I give up.
.................................................
......!!!!!!!!...................................
14:25:49 ** Starting with x^3 + 6 x^2 - 7 x = 0 factor x out of the left-hand side: x(x^2 + 6x - 7) = 0. Factor the trinomial: x ( x+7) ( x - 1) = 0. Then x = 0 or x + 7 = 0 or x - 1 = 0 so x = 0 or x = -7 or x = 1. **
......!!!!!!!!...................................
RESPONSE --> I came up with -7 and 1, but I didn't know what to do with the first x.
.................................................
......!!!!!!!!...................................
14:34:06 query 1.1.90 (was 1.2.18). Explain how you set up and solved an equation for the problem. Include your equation and the reasoning you used to develop the equation. Problem (note that this statement is for instructor reference; the full statement was in your text) scores 86, 80, 84, 90, scores to ave B (80) and A (90).
......!!!!!!!!...................................
RESPONSE --> My first statement was 80 = (2/3)x + (1/3)[( 86 + 80 + 84 + 90)/4] I wanted to get the average of his test scores first, so then I had 80 = (2/3)x + (1/3)(85) 80 = (2/3) x + 28.33 80 - 28.33 = (2/3)x 51.67 = (2/3)x 77.5 = x 90 = (2/3)x + (1/3)85 90 = (2/3)x + 28.33 90- 28.33 = (2/3)x 61.67 = (2/3)x 92.5 = x
.................................................
......!!!!!!!!...................................
14:34:56 ** This can be solved by trial and error but the only acceptable method for this course, in which we are learning to solve problems by means of equations, is by an equation. Let x be the score you make on the exam. The average of the four tests is easy to find: 4-test average = ( 86 + 80 + 84 + 90 ) / 4 = 340 / 4 = 85. The final grade can be thought of as being made up of 3 parts, 1 part being the test average and 2 parts being the exam grade. We would therefore have final average = (1 * test average + 2 * exam grade) / 3. This gives us the equation final ave = (85 + 2 * x) / 3. If the ave score is to be 80 then we solve (85 + 2 * x) / 3 = 80. Multiplying both sides by 3 we get 85 + 2x = 240. Subtracting 85 from both sides we have 2 x = 240 - 85 = 155 so that x = 155 / 2 = 77.5. We can solve (340 + x) / 5 = 90 in a similar manner. We obtain x = 92.5. Alternative solution: If we add 1/3 of the test average to 2/3 of the final exam grade we get the final average. So (using the fact that the test ave is 85%, as calculated above) our equation would be 1/3 * 85 + 2/3 * x = final ave. For final ave = 80 we get 1/3 * 85 + 2/3 * x = 80. Multiplying both sides by 3 we have 85 + 2 * x = 240. The rest of the solution goes as before and we end up with x = 77.5. Solving 1/3 * 85 + 2/3 * x = 90 we get x = 92.5, as before. **
......!!!!!!!!...................................
RESPONSE --> ok
.................................................
......!!!!!!!!...................................
14:36:58 query 1.1.82 (was 1.1.90). Explain, step by step, how you solved the equation v = -g t + v0 for t.
......!!!!!!!!...................................
RESPONSE --> Since I am solving for t, I needed to get the t alone. v - vO = -gt Then I divide by g to solve for t. (v - vO)/g = t
.................................................
......!!!!!!!!...................................
14:37:28 ** NOTE: v0 stands for v with subscript 0; the whole expression v0 stands for the name of a variable. It doesn't mean v * 0. Starting with v = -g t + v0, add -v0 to both sides to get v - v0 = -gt. Divide both sides by -g to get (v - v0) / (-g) = t }or so that t = -(v - v0) / g = (-v + v0) / g.
......!!!!!!!!...................................
RESPONSE --> Forgot to stick in my negative.
.................................................
......!!!!!!!!...................................
14:38:09 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
......!!!!!!!!...................................
RESPONSE --> Fun stuff!
.................................................