Okay, so I've been stuck on a math question for a while now, and I can't seem to figure it out for the life of me. This is kind of embarrassing, considering it looks so simple, but I keep plugging in so many different numbers with none of them making the inequality even. I'm not even necessarily asking for the answer, just some tips on how to solve this would work. A step-by-step would work too! I want to be able to understand this.
Lots of other auto-generated sources are telling me that x = 2, but whenever I try to plug in 2, it still doesn't work. Please help!
12(x − 2) + 3x = 1/2(x + 6) + 2
12(x − 2) + 3x = 1/2(x + 6) + 2
12x - 24 + 3x = 1/2x + 3 + 2
Combine like terms.
15x - 1/2x = 24 + 5
14 1/2x = 29
x = 29/14 1/2
x = 2
distribute the coefficients ... 12x - 24 + 3x = 1/2 x + 3 + 2
collect like terms ... 15x - 24 = 1/2 x + 5
solve ... 29/2 x = 29
yes , x does equal 2
Huh? Try x=2
12(x − 2) + 3x = 1/2(x + 6) + 2
x-2=0, so
3*2 = 1/2 (2+6) + 2
6 = 4+2
seems legit to me
No problem at all! I can definitely help you with solving this equation step by step.
To begin with, let's simplify and expand both sides of the equation to make it easier to work with.
On the left side, distribute the 12 to the terms inside the parentheses:
12(x - 2) + 3x = 1/2(x + 6) + 2
12x - 24 + 3x = (1/2)x + 3 + 2
Now, combine like terms on both sides of the equation:
15x - 24 = (1/2)x + 5
Next, let's get rid of any fractions by multiplying every term in the equation by 2:
2(15x - 24) = 2((1/2)x + 5)
30x - 48 = x + 10
Now, we have an equation without fractions. Let's isolate the variable 'x' by grouping all the x terms on one side and the constant terms on the other side.
Subtract 'x' from both sides of the equation:
30x - x - 48 = x - x + 10
Simplify:
29x - 48 = 10
To isolate 'x', let's get rid of the constant term (-48) by adding 48 to both sides of the equation:
29x - 48 + 48 = 10 + 48
Simplify:
29x = 58
Finally, solve for 'x' by dividing both sides of the equation by 29:
29x/29 = 58/29
Simplify:
x = 2
So the solution to the equation is x = 2.
Now, let's double-check our work by substituting the value of 'x' back into the original equation:
12(x - 2) + 3x = 1/2(x + 6) + 2
When x = 2:
12(2 - 2) + 3(2) = 1/2(2 + 6) + 2
Simplifying:
0 + 6 = 1/2(8) + 2
6 = 4 + 2
6 = 6
Since both sides of the equation are equal when x = 2, we can conclude that the solution is correct.
I hope this explanation helps you understand how to solve this type of equation! If you have any more questions, feel free to ask.