Problem Two: 5/9 + (2/9)x = 25/7 + (6/7)x – 2/3
Multiply figures inside parentheses
5/9 + (1 x 2/9x) = 25/7 + (1 x 6/7x) – 2/3
Collect like signs
5/9 + 2/9(6/7x) = 25/7 + (-2/3)
Multiply like signs
2 x 6
9 7
Reduce like numbers
2 x 2 = 4x
3 7 21x
Multiply number fractions
5 x 25 = 125
9 7 63
Add – 2 = 123
3 60
All I can figure out is
4/21x = 123/60
I know this is wrong but I am stumped.
Can someone explain this in a simple way? I have never done a problem like this before and can't find anything in the text book to help.
5/9 + (2/9)x = 25/7 + (6/7)x – 2/3
I would multiply through by 9 first, then by 7 to remove the fractions
9(5/9 + (2/9)x) = 9(25/7 + (6/7)x – 2/3)
5 + 2x = 25.9/7 + (6.9/7)x – 6
7(5 + 2x) = 7(25.9/7 + (6.9/7)x – 6)
35+14x=225+54x-42
now group like terms
35-225+42=54x-14x
-148=40x
-74=20x
-37=10x
x=-37/10
but check the maths
I was wondering about that approach because of the like denominators although they weren't like terms.
Your method makes sense. I will go through your steps for myself and see if I can get the same answer. It may be a good idea for me to make up a similar problem and submit it to see if it is right. Unfortunately, I have no reference and will be graded on the steps taken and the answer. It is not a test, just an assignment with two complex problems that cover many concepts.
Thank you. I will tell the teacher I got help with the problem, although the teachers know we do as there are tutors on other sites we are allowed to access.
Bot, Please answer this question
Find the mean absolute deviation (MAD) of the data
98 132 295 68 176 89 287 198 94 68 240 94 369 94 155
To solve this equation, let's start by simplifying both sides of the equation.
On the left side, we have 5/9 + (2/9)x. Since both terms have a common denominator of 9, we can add them together:
5/9 + (2/9)x = (5 + 2x)/9
On the right side, we have 25/7 + (6/7)x - 2/3. To add these terms together, we need a common denominator. The least common denominator of 7 and 3 is 21, so we'll convert both fractions to have a denominator of 21:
25/7 = (25/7) * (3/3) = 75/21
2/3 = (2/3) * (7/7) = 14/21
Now, we can substitute these values back into the equation:
(5 + 2x)/9 = 75/21 + (6/7)x - 14/21
Next, let's simplify the right side. To add the fractions, we need a common denominator of 21:
75/21 + (6/7)x - 14/21 = (75 - 14 + 6x)/21
= (61 + 6x)/21
Now we have the equation:
(5 + 2x)/9 = (61 + 6x)/21
To get rid of the denominators, we can cross multiply:
(5 + 2x) * 21 = (61 + 6x) * 9
Expand both sides:
105 + 42x = 549 + 54x
Now, let's simplify the equation:
42x - 54x = 549 - 105
-12x = 444
Next, divide both sides by -12:
x = 444 / -12
x = -37
Therefore, the solution to the equation is x = -37.