Question

7|x -9| -5 = -3|x -9| + 257∣x−9∣−5=−3∣x−9∣+25

Choose 1 answer:


(Choice A)
A
Only x=6x=6x, equals, 6

(Choice B)
B
Only x=12x=12x, equals, 12

(Choice C)
C
x=6x=6x, equals, 6 or x=12x=12x, equals, 12

(Choice D)
D
Only x=-6x=−6x, equals, minus, 6

(Choice E)
E
There are no solutions

Answer 1

To solve the equation, distribute and simplify, combine like terms, isolate the variable, and solve for x.

Step-by-step explanation:

To solve the given equation: 7|x - 9| - 5 = -3|x - 9| + 25

First, rewrite the equation without absolute value notation:

7(x - 9) - 5 = -3(x - 9) + 25

Next, distribute and simplify:

7x - 63 - 5 = -3x + 27 + 25

Combine like terms:

7x - 68 = -3x + 52

Add 3x to both sides:

10x - 68 = 52

Add 68 to both sides:

10x = 120

Divide both sides by 10:

x = 12

So the solution to the equation is x = 12.