3x+8 over 5 + 7/5= -7x over 4
(3x+8)/5 + 7/5 = -7x/4
Multiply both sides by 20:
4(3x+8) + 28 = -35x
12x + 32 + 28 = -35x
12x + 35x = -60
47x = -60
X = - 60/47 = -1 13/47.
To solve this equation, we need to isolate the variable x. Let's break down the steps:
Step 1: Combine like terms
Combine the terms on both sides of the equation.
On the left side, we have 3x + 8/5, and on the right side, we have 7/5 - 7x/4.
Step 2: Get rid of fractions
To simplify the equation, we can multiply all terms by a common denominator. Since the denominators are 5 and 4, the least common multiple is 20.
Multiply each term by 20 to clear the fractions:
20(3x + 8/5) = 20(7/5 - 7x/4)
After simplifying, we get:
20(3x) + 20(8/5) = 20(7/5) - 20(7x/4)
60x + 32 = 28 - 35x
Step 3: Collect the x terms on one side
Move all the terms containing x to one side. In this case, let's add 35x to both sides:
60x + 35x + 32 = 28 - 35x + 35x
Simplifying further:
95x + 32 = 28
Step 4: Solve for x
To solve for x, we need to isolate the variable. Let's subtract 32 from both sides:
95x + 32 - 32 = 28 - 32
Simplifying:
95x = -4
Finally, divide both sides by 95 to solve for x:
x = -4/95
Therefore, the solution to the equation is x = -4/95.