Question:
Bradley wrote the beginning of an equation, [tex]\frac{3}{8}x + 12 =[/tex]
Finish the equation so that the equation will have no solution. Explain how you know.
Answer:
[tex]\frac{3}{8}x + 12 =\frac{3}{8}x -4[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{8}x + 12 =[/tex]
Required
Complete the equation to have no solution
The given equation is a linear equation in form of [tex]mx + b[/tex]
Where [tex]m = \frac{3}{8}[/tex]
Compare both equations
[tex]\frac{3}{8}x + 12 = mx + b[/tex]
Substitute [tex]\frac{3}{8}[/tex] for m
[tex]\frac{3}{8}x + 12 = \frac{3}{8}x + b[/tex]
Collect Like Terms
[tex]b = \frac{3}{8}x - \frac{3}{8}x + 12[/tex]
[tex]b = 12[/tex]
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.
[tex]b \ne 12[/tex]
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
[tex]\frac{3}{8}x + 12 = mx + b[/tex]
Substitute -4 for b and 3/8x for m. This gives:
[tex]\frac{3}{8}x + 12 =\frac{3}{8}x -4[/tex]
