here are the problems i need help with. can u tell me the steps to solve these problems?? thank you!
first problem: a(x+b)=c
second problem: 9x+2a=-3a+4x
here are the problems i need help with. can u tell me the steps to solve these problems?? thank you!
first problem: a(x+b)=c
second problem: 9x+2a=-3a+4x
Hi student897!
What do you mean? Solving for x?
In this case
1) a(x+b) = c
a*x+a*b = c
minus a*b
a*x = c-a*b
divide by a (a is not equal to 0 )
$\displaystyle x = \frac{c-a*b}{a}$
$\displaystyle x = \frac{c}{a}-\frac{a*b}{a}$
$\displaystyle x = \frac{c}{a}-b$
2) 9x+2a=-3a+4x
minus 2a
9x = -3a+4x - 2a
9x = -3a-2a + 4x
9x = -5a + 4x
minus 4x
9x-4x = -5a
5x = -5a
divide by 5
x = -a
Do you understand?
Yours
Rapha
" divide by a (a is not equal to 0 ) "
This is extremely important and a cause for many errors when solving equations.
That being said, the trick is to try to get X alone on one side. Divide, add, remove as much as you have to until it's just X = .....
Might be helpful to repeat some of the basic rules;
$\displaystyle
a(b + c) = a \cdot b + a \cdot c
$
$\displaystyle
d(e - f) = d \cdot e - d \cdot f
$
The basic idea is to "undo" whatever has been done to x. In the first problem, I see that two things have been done to x: first b is added to it, then that sum is multiplied by a. We can "undo" that by doing the opposite, in the opposite order: The opposite of "add b" is to subtract b and the opposite of "multiply by a" is to divide by a. And, since I do this in the opposite order, I first divide by a then subtract b. And, of course, whatever I do on one side of the equation, I do on the other to keep them "balanced".
Starting from a(x+ b)= c and dividing both sides by a, a(x+b)/a= c/a or x+ b= c/a since "a/a"= 1. Subtracting b from both sides, x+ b- b= c/a- b or x= c/a- b since b- b= 0.
You may notice that this is not exactly what Rapha did. He chose to "multiply" out a(x+b)= ax+ ab first. But the answer is the same, of course.
The second, 9x+2a=-3a+4x, is slightly more complicated because it has "x" on both sides. We can fix that by getting rid of the "x" on the right- subtract 4x from both sides: 9x+ 2a- 4x= -3a+ 4x- 4x is the same as 5x+ 2a= -3a. Now that has x multiplied by 5 and then 2a added. The opposite of that is "subtract 2a" and then "divide by 5": 5x+ 2a- 2a= -3a- 2a is the same as 5x= -5a. Now divide both sides by 5: 5x/5= -5a/5 is the same as x= -a.