Answer
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Hint: We use multiplication to solve the LHS of the equation first and then shifting values to suitable sides make an equation where variable is on one side and constant value is on other. We find the value of the variable in the equation and as there is only one unknown variable, i.e. ‘p’ we evaluate the equation for the value of ‘p’.
Complete step-by-step solution:
We have to solve the equation \[4 + 5(p - 1) = 34\].......................… (1)
Since here the variable is ‘p’ in the equation, we will find the value of ‘p’ using operations like multiplication, addition, subtraction and division.
Solve LHS of the equation (1)
Multiply the terms required in the left hand side of the equation
\[ \Rightarrow 4 + 5 \times p - 5 \times 1 = 34\]
Calculate the product in left hand side of the equation
\[ \Rightarrow 4 + 5p - 5 = 34\]
Group the constants in left hand side of the equation
\[ \Rightarrow \left( {4 - 5} \right) + 5p = 34\]
Calculate the value of bracket containing constant terms in left hand side of the equation
\[ \Rightarrow - 1 + 5p = 34\]
Shift all constants to right hand side of the equation
\[ \Rightarrow 5p = 34 + 1\]
Calculate the sum in right hand side of the equation
\[ \Rightarrow 5p = 35\]
Divide both sides of the equation by 5
\[ \Rightarrow \dfrac{{5p}}{5} = \dfrac{{35}}{5}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow p = 7\]
So, the value of \[p = 7\]for the equation\[4 + 5(p - 1) = 34\]
\[\therefore \]Solution of the equation \[4 + 5(p - 1) = 34\] is \[p = 7\]
Note: Linear equations in one variable is used when there is only one unknown variable. Linear equations in two variables are used when there are two unknown variables.
Complete step-by-step solution:
We have to solve the equation \[4 + 5(p - 1) = 34\].......................… (1)
Since here the variable is ‘p’ in the equation, we will find the value of ‘p’ using operations like multiplication, addition, subtraction and division.
Solve LHS of the equation (1)
Multiply the terms required in the left hand side of the equation
\[ \Rightarrow 4 + 5 \times p - 5 \times 1 = 34\]
Calculate the product in left hand side of the equation
\[ \Rightarrow 4 + 5p - 5 = 34\]
Group the constants in left hand side of the equation
\[ \Rightarrow \left( {4 - 5} \right) + 5p = 34\]
Calculate the value of bracket containing constant terms in left hand side of the equation
\[ \Rightarrow - 1 + 5p = 34\]
Shift all constants to right hand side of the equation
\[ \Rightarrow 5p = 34 + 1\]
Calculate the sum in right hand side of the equation
\[ \Rightarrow 5p = 35\]
Divide both sides of the equation by 5
\[ \Rightarrow \dfrac{{5p}}{5} = \dfrac{{35}}{5}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow p = 7\]
So, the value of \[p = 7\]for the equation\[4 + 5(p - 1) = 34\]
\[\therefore \]Solution of the equation \[4 + 5(p - 1) = 34\] is \[p = 7\]
Note: Linear equations in one variable is used when there is only one unknown variable. Linear equations in two variables are used when there are two unknown variables.