Question

Solve the following equations and check your results. If $5x + 9 = 5 + 3x$, then x =
A. 1
B. -2
C. -7
D. 3

Answer 1

Hint: Take variable terms to one side and constant terms to the other side and then solve them to find the value of x. To check your solution, place the value of x that you found out into the original equation and if the values of both sides come to be equal, then your solution is correct.

Complete step by step solution:
When solving algebraic equations, the most important thing is to bring all the variables to one side and constants to the other side. After doing that, we need to solve the equation and find the value of the variable.
Let’s move to the equation directly and see how it works.
$\
  5x + 9 = 5 + 3x \\
  5x - 3x = 5 - 9 \\
  2x = - 4 \\
  x = - 2 \\
\ $
Now from this equation, we see from the second step that when we take one thing from one side of the equation to the other side, the sign changes which means that if it were positive, it will be negative on the other side and if it were negative, it will be positive on the other side.
Look at how when ‘+3x’ goes from the right-hand side to the left-hand side, it becomes ‘-3x’ and when ‘+9’ goes from the left-hand side to the right-hand side, it becomes ‘-9’.
Now that we have the value of x which is -2, let us put it in the original equation and check it.
$\
  5x + 9 = 5 + 3x \\
  5 \times \left( { - 2} \right) = 5 + 3 \times \left( { - 2} \right) \\
   - 10 + 9 = 5 - 6 \\
   - 1 = 1 \\
\ $
We see that the left side is equal to the right side which is -1. As such, we can say that our result is correct. If both sides were not equal, we would have had to check the equation again because the solution in that case is surely wrong.

Note:
Whenever working with such equations, if you are not confident in removing anything from one side to the other side, you can subtract one term from both sides without changing the equality. For example, in the question first subtract 3x from both sides and then subtract 9 from both sides and we will have the same equation.
$\
  5x + 9 = 5 + 3x \\
\Rightarrow 5x + 9 - 3x = 5 + 3x - 3x \\
\Rightarrow 2x + 9 = 5 \\
\Rightarrow 2x + 9 - 9 = 5 - 9 \\
\Rightarrow 2x = - 4 \\
\Rightarrow x = - 2 \\
\ $