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Consider solving the equation for x

3(3x+4)-5=ax+b
which statements are true about the solution to the equation when substituting values for a and b as specified?
select all that apply

User Darryn
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1 Answer

3 votes

The statement that are true about the solution to the equation when substituting values for a and b as specified are;

  • A. If a=−3 and b=4 , then there is exactly one solution to the equation.
  • C. If a=9 and b=−2 , then there is no solution to the equation.

Which statements are true about the solution to the equation when substituting values for a and b as specified?

3(3x + 4) - 5 = ax + b

9x + 12 - 5 = ax + b

9x + 7 = ax + b

9x - ax = b - 7

x(9 - a) = b - 7

Check all options:

A. If a=−3 and b=4 , then there is exactly one solution to the equation.

x(9 - a) = b - 7

x(9 - -3) = 4 - 7

x(9+3) = -3

x(12) = -3

x = -3/12

x = -1/4

True

B. If a=−9 and b=13 , then there is no solution to the equation.

x(9 - a) = b - 7

x(9- -9) = 13 - 7

x(9+9) = 6

x(18) = 6

x = 6/18

x = 1/3

False

C. If a=9 and b=−2 , then there is no solution to the equation.

x(9 - a) = b - 7

x(9 - 9) = -2 - 7

x(0) = -9

x = -9/0

True

D. If a=−3 and b=−5 , then there are infinitely many solutions to the equation.

x(9 - a) = b - 7

x(9 - -3) = -5 - 7

x(9 + 3) = -12

x(12) = -12

x = -12/12

x = -1

False

Complete question:

3(3x + 4) - 5 = ax + b

Which statements are true about the solution to the equation when substituting values for a and b as specified?

Select all that apply.

A. If a=−3 and b=4 , then there is exactly one solution to the equation.

B. If a=−9 and b=13 , then there is no solution to the equation.

C. If a=9 and b=−2 , then there is no solution to the equation.

D. If a=−3 and b=−5 , then there are infinitely many solutions to the equation.

User Bae Cheol Shin
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7.9k points