solve for x in the following.
(a) 3/4x+5/6x=5x-125/3
(b) 2(3x-7)+4(3x+2)=6(5x+9)+3
3/4x+5/6x=5x-125/3
the LCD is 12, so multiply each term by 12
9x + 10x = 60x - 500
easy from here....
2(3x-7)+4(3x+2)=6(5x+9)+3
6x - 14 + 12x + 8 = 30x + 54 + 3
I am sure you an handle it from here
please Reiny i struggle from there
To solve for x in both equations, we need to simplify and isolate the variable on one side of the equation. Let's solve them step by step:
(a) 3/4x + 5/6x = 5x - 125/3
First, let's get rid of the denominators by multiplying every term by the least common multiple (LCM) of the denominators, which is 12. Multiply each term by 12:
(12)(3/4x) + (12)(5/6x) = (12)(5x) - (12)(125/3)
9x + 10x = 60x - 500
Combine similar terms:
19x = 60x - 500
Next, let's simplify further by moving all the terms involving x to one side and the constant terms to the other side:
-41x = -500
Finally, solve for x by dividing both sides of the equation by -41:
x = -500 / -41
So, the solution for x in equation (a) is x ≈ 12.195.
(b) 2(3x - 7) + 4(3x + 2) = 6(5x + 9) + 3
Start by distributing each of the coefficients:
6x - 14 + 12x + 8 = 30x + 54 + 3
Combine similar terms:
18x - 6 = 30x + 57
Next, let's simplify further by moving all the terms involving x to one side and the constant terms to the other side:
18x - 30x = 57 + 6
-12x = 63
Finally, solve for x by dividing both sides of the equation by -12:
x = 63 / -12
Therefore, the solution for x in equation (b) is x ≈ -5.25.