Question

Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.

The square root of the quantity 11 x plus 5 end quantity equals 7.

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3 weeks 2022-12-21T07:00:04+00:00 2 Answers 0 views 0

1. Answer: x =4, not extraneous.
Explanation:
$$\sqrt{11x + 5} = 7$$, square all sides.
Because the square root is squared, it is reversed: $$11x+5 =7^{2}$$
(72 = 49)
Subtract 5 from all sides: 11x = 44
(49 – 5 = 44)
(11x is an unknown so we cannot subtract 5 from it)
To get rid of the unknown, divide 11 on all sides: x = 4
(11x ÷ 11 = 1, x is written as one) (44 ÷ 11 = 4)
x = 4
The solution is not extraneous.

Step-by-step explanation:
\sqrt{11x+5}
11x+5
= 7 ( square both sides )
11x + 5 = 7² = 49 ( subtract 5 from both sides )
11x = 44 ( divide both sides by 11 )
x = 4
substitute x = 4 into the left side of the equation and if equal to the right side , then it is the solution.
\sqrt{11(4)+5}
11(4)+5
= \sqrt{44+5}
44+5
= \sqrt{49}
49
= 7 ← equals right side
then x = 4 is the solution