Question

Solve
\[\dfrac{{3x}}{4} - \dfrac{7}{4} = 5x + 12\]?

Answer 1

Hint: Here we need to solve for ‘x’. First, we take LCM on the Left-hand side of the equation and we simplify it. Then we can solve for ‘x’ using the transposition method. That is separating the variables on one side of the equation and the constant on the other side.

Complete step-by-step answer:
Given, \[\dfrac{{3x}}{4} - \dfrac{7}{4} = 5x + 12\].
Now Taking LCM and simplifying we have,
\[\dfrac{{3x - 7}}{4} = 5x + 12\]
Now multiplying 4 on both side of the equation,
\[3x - 7 = 4\left( {5x + 12} \right)\]
Expanding the brackets
\[3x - 7 = 20x + 48\]
We transpose ‘-7’ which is present on the left-hand side of the equation to the right-hand side of the equation by adding ‘7’ on the right-hand side of the equation.
\[3x = 20x + 48 + 7\]
Now transposing ‘20x’ to the left-hand side by subtracting ‘20x’ on the left-hand side of the equation.
\[3x - 20x = 48 + 7\]
\[ - 17x = 55\]
\[ \Rightarrow x = - \dfrac{{55}}{{17}}\].This is the exact form.
\[ \Rightarrow x = - 3.235\]. This is the decimal form.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem. In this we have a decimal value, it will be difficult to verify in this problem. In the above, we did the transpose of addition and subtraction. Similarly, if we have multiplication, we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.