Question

-BRAINLIEST IF ANSWERED RIGHT-

Given the equation
5+x−12=x−7:

Part A. Solve the equation
5+x−12=x−7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values
x=−4,0,5 to verify your solution to the equation
5+x−12=x−7.
In your final answer, include all of your calculations.

Answer 1

Answer:

Part A:

$x\in \mathbb{R}$ ($x$ is equal to all real numbers)

Part B:

$5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark$

Step-by-step explanation:

Part A:

Given $5+x-12=x-7$, combine like terms:

$x-7=x-7$

Add 7 to both sides:

$x=x$

Since this is merely a true statement for all real numbers (reflexive property), this equation is true for any real value of $x$.

Therefore,

$x\in \mathbb{R}$ ($x$ is equal to all real numbers).

Part B:

Using arbitrary values $x=-4, x=0, x=5$ as requested in part B, verify:

$5+(-4)-12=-4-7,\\-11=-11\:\checkmark,\\\\5+0-12=0-7,\\-7=-7\:\checkmark,\\\\5+5-12=5-7,\\-2=-2\:\checkmark$