Question

How do you solve \[5x - 1 = 3x + 7\] ?

Answer 1

Hint: Solve the given equation i.e. bring all variable values together on one side and all constant values together on the other side. Cancel possible terms and write the equation in simplest form. In the end the equation will give the value of ‘x’ being equal to constant.

Complete step-by-step solution:
We are given the equation \[5x - 1 = 3x + 7\]
Since the equation has only one variable i.e. x, we will calculate the value of x.
Shift all variable values to the left hand side of the equation and all constant values to the right hand side of the equation.
\[ \Rightarrow 5x - 3x = 7 + 1\]
Calculate the values on both sides of the equation
\[ \Rightarrow 2x = 8\]
Cancel same factors from both sides of the equation i.e. 2
\[ \Rightarrow x = 4\]

Solution of the equation \[5x - 1 = 3x + 7\] is \[x = 4\]

Note: Alternate method:
We can write right hand side of the equation by breaking the variable term
\[5x - 1 = 3x + 7\] becomes \[3x + 2x - 1 = 3x + 7\]
Cancel same terms from both sides of the equation i.e. 3x
The equation becomes \[2x - 1 = 7\]
Shift constant value to right hand side
\[ \Rightarrow 2x = 7 + 1\]
\[ \Rightarrow 2x = 8\]
Cancel same factors from both sides of the equation i.e. 2
\[ \Rightarrow x = 4\]
\[\therefore \]Solution of the equation \[5x - 1 = 3x + 7\] is \[x = 4\]