Question

Bradley wrote the beginning of an equation, 3··8x 1 12 5 u. Part A Finish the equation so that the equation will have no solution. Explain how you know.

Answer 1

Question:

Bradley wrote the beginning of an equation, $\frac{3}{8}x + 12 =$  

Finish the equation so that the equation will have no solution. Explain how you know.

Answer:

$\frac{3}{8}x + 12 =\frac{3}{8}x -4$

Step-by-step explanation:

Given

$\frac{3}{8}x + 12 =$  

Required

Complete the equation to have no solution

The given equation is a linear equation in form of $mx + b$

Where $m = \frac{3}{8}$

Compare both equations

$\frac{3}{8}x + 12 = mx + b$

Substitute $\frac{3}{8}$ for m

$\frac{3}{8}x + 12 = \frac{3}{8}x + b$

Collect Like Terms

$b = \frac{3}{8}x - \frac{3}{8}x + 12$

$b = 12$

This implies that, for the equation to have a solution the value of b must be 12.

However, for the equation not to have a solution, the value of b must not equal 12

i.e.

$b \ne 12$

This implies that, we can assume any value, other than 12 for b so that the equation will not have a solution.

Say for instance: b = -4

$\frac{3}{8}x + 12 = mx + b$

Substitute -4 for b and 3/8x for m. This gives:

$\frac{3}{8}x + 12 =\frac{3}{8}x -4$