Question

Solve:\[4 - (2(z - 4))/2 = 1(2z + 5)\]

Answer 1

Hint: If any equation involves only one variable and the highest order of the variable is one, then that equation is said to be a linear equation. Here we will simplify the equation by using the basic mathematical operations and will find the value of the unknown term or the variable “z”.

Complete step-by-step answer:
Take the given equation –
\[4 - (2(z - 4))/2 = 1(2z + 5)\]
Rewrite the above equation –
\[4 - \dfrac{{(2(z - 4))}}{2} = 1(2z + 5)\]
Same terms from the denominator and the numerator cancel each other. Therefore, remove from the numerator and the denominator.
\[ \Rightarrow 4 - (z - 4) = 1(2z + 5)\]
Open the brackets multiplying the constant terms if any as such on the right hand side of the equation. Also, remember that minus signs outside the bracket change the sign of the terms inside the bracket once it is opened. Negative terms are changed to positive and positive terms are changed to negative.
\[ \Rightarrow 4 - z + 4 = 2z + 5\]
Bring all the variables at one side and the constants on the other side of the equation – Also; remember that the sign of the term is changed when moved from one to another. Positive changes to negative and negative changes to positive.
\[ \Rightarrow 4 + 4 - 5 = 2z + z\]
Simplify the above equation –
\[
   \Rightarrow 8 - 5 = 3z \\
   \Rightarrow 3 = 3z \;
 \]
When the term in the multiplicative at one side, moved to another side of the equation, then it goes to the denominator-
 $ \Rightarrow z = \dfrac{3}{3} $
Same terms from the numerator and the denominator cancel each other,
 $ \Rightarrow z = 1 $ is the required answer.
So, the correct answer is “z = 1”.

Note: Remember the difference between the two most commonly used concepts in mathematics, the variables and the constant. Variable is the value which has the ability to change whereas, the constants are the terms which remain unchanged and have the fixed value.