Define variable value - General Math

Question

I met a little problem in one of my Math - tasks. Its quite simple:

I get to cases =

case 1: $(476\cdot x)+220$

case 2: $(278\cdot x)+675$

The variable x have to be a value, so case 1 and case 2 equals the same, so:

$(476\cdot x)+220 = (278\cdot x)+675$

How do I solve this?

Thanks in advance.

Oliver

Answer 1

If in fact there is some value $a$ such that

case 1 = $(476x)+220 = a$

case 2 = $(278x)+675 = a$,

then it is valid to equate the left-hand side of each of the above equations:

$$476 x + 220 = 278x + 675$$

To solve for $x$, first subtract $278 x$ from each side of the equation.

$$ 476 x - 278 x + 220 = 278x - 278 x + 675 \\ \\ \iff 198x + 220 = 675$$

Then subtract $220$ from each side of the equation:

$$ 198x + 220 - 220 = 675 - 220 \\ \\ \iff 198 x = 455$$

Now divide each side of the equation by $198$:

$$198x = 455 \iff \dfrac {198}{198}x = \dfrac {455}{198}$$

Now simplify, and you'll have solved for $x$.

Answer 2

I don't understand the problem.

$(476*x)+220 = (278*x)+675$

$\implies 198x=455$

$\implies x = 2.298$

what's the issue?