6(3x-2)-3(2x-4)=5(3x+8)-7(2x-3)
show the work please.
For this problem, the distributive property is a must. It states that...
a(b+c) = ab + ac
For example,
3(9+2) = (3)(9) + (3)(2) = 27 + 6 = 33
Usually, we would just do 3(11) = 33, but that is just an example.
7(x+4) = 7x + (7)(4) = 7x + 28
Try to do that in your problem, and we can critique your thinking.
Nuts. You show the work, and we will be happy to critique it. We don't do homework for students.
To solve the given equation, let's first simplify both sides of the equation by distributing the terms:
On the left side, we distribute the 6 and the 3 to the terms inside parentheses:
6(3x-2) - 3(2x-4)
= 18x - 12 - 6x + 12
On the right side, we distribute the 5 and the -7 to the terms inside parentheses:
5(3x+8) - 7(2x-3)
= 15x + 40 - 14x + 21
Now we can simplify further by combining like terms on both sides:
Left side:
18x - 12 - 6x + 12
= (18x - 6x) + (-12 + 12)
= 12x + 0
= 12x
Right side:
15x + 40 - 14x + 21
= (15x - 14x) + (40 + 21)
= x + 61
Now we have simplified the equation to:
12x = x + 61
To solve for x, let's isolate the x terms on one side:
Subtract x from both sides:
12x - x = x + 61 - x
11x = 61
Lastly, divide both sides by 11 to solve for x:
11x/11 = 61/11
x = 61/11
Therefore, the solution to the equation is x = 61/11.