Solve the equation and check the solution.
[tex]$-z-5=-7$[/tex]
Answer (2)
To solve the equation − z − 5 = − 7 , we first add 5 to both sides to isolate − z , resulting in − z = − 2 . Multiplying by -1 gives us z = 2 . The solution is verified by substituting back into the original equation, confirming that z = 2 is correct.
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Add 5 to both sides of the equation: − z − 5 + 5 = − 7 + 5 , which simplifies to − z = − 2 .
Multiply both sides by -1: ( − 1 ) ( − z ) = ( − 1 ) ( − 2 ) .
Simplify to find the value of z : z = 2 .
Check the solution: − 2 − 5 = − 7 , which is true. Therefore, the solution is 2 .
Explanation
Understanding the Problem We are given the equation − z − 5 = − 7 and we want to find the value of z that makes this equation true.
Adding 5 to Both Sides To isolate z , we first add 5 to both sides of the equation: − z − 5 + 5 = − 7 + 5
Simplifying the Equation Simplifying both sides, we get: − z = − 2
Multiplying by -1 Now, we multiply both sides by -1 to solve for z :
( − 1 ) ( − z ) = ( − 1 ) ( − 2 )
Finding the Value of z This simplifies to: z = 2
Checking the Solution To check our solution, we substitute z = 2 back into the original equation: − z − 5 = − 7 − 2 − 5 = − 7 − 7 = − 7
Since the equation holds true, our solution is correct.
Final Answer Therefore, the solution to the equation − z − 5 = − 7 is z = 2 .
Examples
In real life, you might use this type of equation when managing a budget. For example, imagine you are tracking your expenses. If you spent $5 and your account is now 7 in d e b t , yo u c an u se t h ee q u a t i o n -z - 5 = -7 t o f in d o u t h o w m u c hm o n ey , z$, you started with. Solving the equation tells you that you initially had $2.
