Solve 4 (z + 5) = 32.
The solution is z = ☐
The Correct Answer and Explanation is:
We are asked to solve the equation ( 4(z + 5) = 32 ).
Step 1: Distribute the 4
The first step is to apply the distributive property, which states that ( a(b + c) = ab + ac ). In this case, we distribute the 4 to both terms inside the parentheses.
[
4(z + 5) = 4z + 4 \times 5 = 4z + 20
]
Thus, the equation becomes:
[
4z + 20 = 32
]
Step 2: Isolate the variable term
Next, we want to isolate the term with the variable ( z ). To do this, we subtract 20 from both sides of the equation to eliminate the constant term on the left-hand side:
[
4z + 20 – 20 = 32 – 20
]
Simplifying both sides:
[
4z = 12
]
Step 3: Solve for ( z )
Now that we have ( 4z = 12 ), we need to solve for ( z ) by dividing both sides of the equation by 4:
[
\frac{4z}{4} = \frac{12}{4}
]
This simplifies to:
[
z = 3
]
Step 4: Verify the solution
To ensure the solution is correct, we can substitute ( z = 3 ) back into the original equation to check if both sides are equal:
[
4(z + 5) = 32
]
Substitute ( z = 3 ):
[
4(3 + 5) = 32
]
Simplify:
[
4(8) = 32
]
[
32 = 32
]
Since both sides are equal, the solution ( z = 3 ) is correct.
Conclusion
The solution to the equation ( 4(z + 5) = 32 ) is ( z = 3 ).