Question

equations - linear equations: problem 10
solve the equation for x.
a(x - b)=m(x - c).
answer: (x=)
if (a = 1,b = 2,c = 3,) and (m = 4) then what is the value of (x)?
answer: (x=)
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Explanation:

Step1: Expand the equation

$a(x - b)=m(x - v)$ expands to $ax - ab=mx - mv$.

Step2: Group the x - terms

Move all terms with $x$ to one side: $ax - mx=ab - mv$.

Step3: Factor out x

Factor out $x$ on the left - hand side: $x(a - m)=ab - mv$.

Step4: Solve for x

Divide both sides by $(a - m)$ (assuming $a
eq m$) to get $x=\frac{ab - mv}{a - m}$.

If $a = 1$, $b = 2$, $m = 1$, and $v = 3$:

Step1: Substitute the values into the original equation

The original equation $a(x - b)=m(x - v)$ becomes $1\times(x - 2)=1\times(x - 3)$.
Expanding gives $x - 2=x - 3$.
Subtracting $x$ from both sides results in $- 2=-3$, which is a contradiction. This means there is no solution for $x$ when $a = m$.

Answer:

$x=\frac{ab - mv}{a - m}$ (for $a
eq m$), no solution (for $a = m$)