(x+1)/3 + (3x - 2)/4 = (x + 5)/8 - (7x - 1)/6 - 37/12
I need the steps please...I know the answer
first, look for a common denominator. LCM(3,4,8,6,12) = 24
So, multiply it all by 24:
8(x+1) + 6(3x-2) = 3(x+5) - 4(7x-1) - 74
expand the terms:
8x+8+18x-12 = 3x+15-28x+4-74
8x+18x-3x+28x = 15+4-74-8+12
51x = -51
x = -1
Steve, I see it clearly now....thank you
After a few dozen more, these will be no problem.
To solve the given equation, you can follow these steps:
Step 1: Clear the denominators.
Multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 24. This will eliminate the fractions.
24 * [(x+1)/3] + 24 * [(3x - 2)/4] = 24 * [(x + 5)/8] - 24 * [(7x - 1)/6] - 24 * [37/12]
After multiplying, the equation becomes:
8(x + 1) + 6(3x - 2) = 3(x + 5) - 4(7x - 1) - 37(2)
Step 2: Simplify and distribute.
Simplify the equation by using the distributive property and combine like terms.
8x + 8 + 18x - 12 = 3x + 15 - 28x + 4 - 74
Simplifying further, we get:
26x - 4 = -25x - 55
Step 3: Move the variables to one side and the constants to the other side.
Add 25x to both sides and subtract 4 from both sides to move the variables to one side and constants to the other side.
26x + 25x = -55 + 4
Combining like terms, we get:
51x = -51
Step 4: Solve for x.
Divide both sides of the equation by 51 to isolate x.
x = -51 / 51
Simplifying further, we get:
x = -1
Therefore, the solution to the given equation is x = -1.