I need help solving this problem 1/5(2x - 10)+4x= -3(1/5x +4)
Can someone at least walk me through this problem? Please and thanks!
@ms.sue?
1/5(2x - 10)+4x= -3(1/5x +4)
clear parentheses:
2/5 x - 2 + 4x = -3/5 x - 12
Now get all the x stuff on one side:
2/5 x + 4x + 3/5 x = 2-12
2/5 + 3/5 = 1, so
5x = -10
x = -2
Thank you so much!
To solve this problem, we need to simplify the equation and then isolate the variable (x) on one side. Let's go step by step:
Step 1: Distribute the fractions
To distribute the fractions, we can multiply each term within the parentheses by the fraction.
For the left side of the equation:
1/5(2x - 10) = (1/5 * 2x) - (1/5 * 10) = 2/5x - 2
For the right side of the equation:
-3(1/5x + 4) = -3 * (1/5x) - 3 * 4 = -3/5x - 12
After distributing the fractions, our equation becomes:
2/5x - 2 + 4x = -3/5x - 12
Step 2: Combine like terms
Combine the variables (x) on the left side and the constant numbers on the right side of the equation.
On the left side, the like terms are 2/5x and 4x. Adding them together gives us:
(2/5x + 4x) = (2/5 + 20/5)x = 22/5x
On the right side, the like terms are -3/5x and -12. Adding them together gives us:
(-3/5x - 12) = -3/5x - 60/5 = -63/5x
After combining like terms, our equation becomes:
22/5x = -63/5x - 12
Step 3: Isolate the variable
To isolate the variable (x), we want to get rid of the fraction coefficients. We can do this by multiplying both sides of the equation by the least common denominator (LCD), which is the product of the denominators of the fractions involved. In this case, the LCD is 5, since both fractions have 5 as their denominator.
Multiplying both sides of the equation by 5, we have:
5 * (22/5x) = 5 * (-63/5x - 12)
Simplifying further:
22x = -63x - 60
Step 4: Solve for x
To solve for x, we want to isolate it on one side of the equation.
Add 63x to both sides to move the variable terms to one side:
22x + 63x = -60
Combine like terms:
85x = -60
Finally, divide both sides by 85 to solve for x:
x = -60/85
Now, simplify the fraction if possible. Both the numerator and the denominator have a common factor of 5. Dividing -60 by 5 and 85 by 5, we have:
x = -12/17
So the solution to the equation is x = -12/17.