Question

interpreting the value of an unknown

transform the equation to isolate (x): (ax = bx + 1). how is the value of (x) related to the difference of (a) and (b)?

Explanation:

Group terms containing x

Using the Literal Equations and Algebraic Rearrangement knowledge points, we subtract \(bx\) from both sides:

$$ ax - bx = 1 $$

Factor out the variable x

Using the Distributive Property knowledge point, we factor \(x\) from the left side:

$$ x(a - b) = 1 $$

Isolate the variable x

Divide both sides by the difference \((a - b)\):

$$ x = \frac{1}{a - b} $$

Analyze the relationship

The value of \(x\) is the reciprocal of the difference of \(a\) and \(b\). This means \(x\) is inversely proportional to the difference \((a - b)\).

Answer:

The isolated equation is:

$$x = \frac{1}{a - b}$$

The value of \(x\) is the reciprocal of the difference of \(a\) and \(b\) (meaning \(x\) is inversely proportional to the difference \(a - b\)).