Question

equations-linear equations: problem 10 (1 point) solve the equation for x (x(a - b)=m(x - c)). answer: (x=) if (a = 1,b = 7,c = 1), and (m = 2) then what is the value of x? answer: (x=) note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining.

Explanation:

Step1: Expand both sides

$x(a - b)=ax - bx$ and $m(x - c)=mx - mc$, so $ax - bx=mx - mc$.

Step2: Move terms with $x$ to one - side

$ax - bx - mx=-mc$.

Step3: Factor out $x$

$x(a - b - m)=-mc$.

Step4: Solve for $x$

$x=\frac{mc}{b + m - a}$.

Answer:

For the first part: $x=\frac{mc}{b + m - a}$
For the second part: Substitute $a = 1$, $b = 7$, $c = 1$, and $m = 2$ into $x=\frac{mc}{b + m - a}$.
$x=\frac{2\times1}{7 + 2-1}=\frac{2}{8}=\frac{1}{4}$

So the answers are:
$x=\frac{mc}{b + m - a}$
$x=\frac{1}{4}$