Question

Solve for x: z(14x−2y)=7 if z equals 0 Solve for x: z(14x−2y)=7 if z does not equal 0

Answer 1

Answer:

• $z = 0$; x doesn't have a solution

• $z\neq 0$; $x = \frac{1}{14}(\frac{7}{z} + 2y)$

Step-by-step explanation:

Given

$z(14x -2y)=7$

Required;

Solve for x, when

• $z = 0$

• $z\neq 0$

$z(14x -2y)=7$

Divide both sides by z

$\frac{z(14x -2y)}{z} = \frac{7}{z}$

$14x -2y = \frac{7}{z}$

Add 2y to both sides

$14x -2y + 2y= \frac{7}{z} + 2y$

$14x = \frac{7}{z} + 2y$

Divide both sides by 14

$\frac{14x}{14} = \frac{1}{14}(\frac{7}{z} + 2y)$

$x = \frac{1}{14}(\frac{7}{z} + 2y)$

The above expression is the value of x when $z\neq 0$

To solve for when z = 0, we simply substitute 0 for z

$x = \frac{1}{14}(\frac{7}{z} + 2y)$

$x = \frac{1}{14}(\frac{7}{0} + 2y)$

0 cant't divide any number; hence, from the above expression we conclude that

$x = \ u\ n\ d\ e \ f\ i \ n\ e\ d$

or

x doesn't have a solution