Question

select all values for b that make the equation 8(x - 3) = 2x + b + 6x have no solutions for x. -24 -3 3 24​

Answer 1

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Answer:
`\textsf{B (-3), C (3), and D (24)}`

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Given:
`\textsf{8(x - 3) = 2x + b + 6x}`

Find:
`\textsf{Which values for b are not a solution}`

Solution: In order to make it easier for us to determine the answer, let us first simplify the expression that was given to us. We can do that by first combining like terms on the right side of the equation and distributing the 8 on the left side of the equation.

• 
  `\textsf{8(x - 3) = 2x + b + 6x}`

• 
  `\textsf{(8 * x) + (8 * -3) = 8x + b}`

• 
  `\textsf{8x - 24 = 8x + b}`

We can now subtract 8x from both sides of the equation.

• 
  `\textsf{8x - 8x - 24 = 8x - 8x + b}`

• 
  `\textsf{-24 = b}`

Now that we know that b is equal to -24, that means that any value other than -24 would cause the equation to have no solutions. Therefore, the correct answer would be B (-3), C (3), and D (24).