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“Consider the equation 2(4x - 5) = ax + 2. What value of a makes the equation have NO SOLUTION?”

please help, I desperately need it.

User Anita C
by
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1 Answer

3 votes

answer :

8

steps:

NO SOLUTION means something like where the equation is

0 = 12

where number on the left of the equal sign is different from the number on the right of the equal sign

Okay, let's solve this step-by-step:

2(4x - 5) = ax + 2

Distribute the 2 on the left side:

8x - 10 = ax + 2

Group the x terms together:

8x - ax = 10 + 2

Combine like terms:

8x - ax = 12

Add ax to both sides:

8x = ax + 12

Subtract ax from both sides:

8x - ax = 12

Factor out x:

x(8 - a) = 12

For the equation to have no solution, x(8 - a) cannot equal 12 for any value of x. This happens when 8 - a = 0.

So a = 8 is the value that makes the original equation have no solution.

0 = 12

The key is that when a = 8, it causes both sides of the final factored equation to equal 0 for all values of x, meaning there are NO values of x that can satisfy the equation.

metaAI

User Lrrr
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