Question

solve $a(x - b) = c$ for $x$
$ax - ab = c$
$\underline{\quad +ab\quad\quad +ab}$
$\underline{\quad ax\quad = \frac{c + ab}{a}}$
$\boxed{x = \frac{c + ab}{a}}$
what words below match the solution?
hint: what math operations are being shown?
\square x equals the value of c plus a times b all divided by a
\square x equals the value of c minus a times b all divided by b
rewatch

Explanation:

Step1: Analyze the solution

From the steps shown, we first expanded \(a(x - b)\) to get \(ax - ab = c\). Then we added \(ab\) to both sides: \(ax= c + ab\). Then we divided both sides by \(a\) to get \(x=\frac{c + ab}{a}\) (which can also be written as \(x=\frac{c+ a\times b}{a}\)).

Now let's analyze the first option: "x equals the value of c plus a times b all divided by a" - this matches our derived formula \(x=\frac{c + ab}{a}\) (since \(a\times b = ab\)).

The second option: "x equals the value of c minus a times b all divided by b" - the numerator here is \(c - ab\) and the denominator is \(b\), which does not match our solution.

Step2: Confirm the correct option

So the first option is the one that matches the solution for \(x\) when solving \(a(x - b)=c\) for \(x\).

Answer:

The correct option is: x equals the value of c plus a times b all divided by a (with the checkbox next to it marked as correct).