Question

How do you solve $5\left( 4x-1 \right)=2\left( x+3 \right)?$

Answer 1

Hint: We will open the brackets by multiplying the constant terms with terms inside the brackets. Then we will transpose the terms accordingly so that the variable terms lie on the same side and the constant terms lie on the same side. Then we apply the operations present in the equation on the terms. Then if it is necessary, we will transpose the terms again to find the value of the unknown.

Complete step by step solution:
Let us consider the given equation $5\left( 4x-1 \right)=2\left( x+3 \right).$
We need to find the value of the unknown variable $x.$
Let us multiply $5$ with the terms inside the brackets on the LHS and multiply $2$ with terms inside the brackets on the RHS to open the brackets.
We will get $20x-5=2x+6.$
Now, we need to transpose the constant term from the LHS to the RHS of the equation while we transpose the variable term from the RHS to the LHS of the equation.
We will get $20x-2x=6+5.$
In the next step, we will apply the operations subtraction and addition on the terms on the LHS and on the RHS respectively.
So, we will get $18x=11.$
Now, we will transpose $18$ from the LHS to the RHS to get $x=\dfrac{11}{8}.$
Hence the solution of the given equation is $x=\dfrac{11}{18}.$

Note: When you are asked to solve an equation, you are asked to find the value of the unknown variable. When we transpose the terms, positive terms will become negative terms and the terms in the numerator will be shifted to the denominator.