Question

How do you solve \[3x+5=1x+19\]?

Answer 1

Hint: We have an expression which we have to solve. The expression has \[x\] as the only variable. So we have to find the value of \[x\]. We will first subtract 5 from both the sides of the equality and then carry out the required calculation. Next, we will subtract \[x\] from both the sides and solve it up to find the value of \[x\].

Complete step by step solution:
According to the given question, we have an equation in one variable. So, we have to solve the expression in terms of \[x\], that is, we have to find the value of the variable \[x\] in the given expression.
We will start by writing the given expression, we have,
\[3x+5=1x+19\]----(1)
In order to find the value of the variable, we will have to separate the \[x\] terms and the constants. We will, at first, subtract 5 from both sides of the equality in equation (1), we get,
\[\Rightarrow 3x+5-5=1x+19-5\]
In the LHS, 5 gets cancelled and we calculate the expression in the RHS and we get,
\[\Rightarrow 3x=1x+19-5\]
We continue to solve the expression, we get,
\[\Rightarrow 3x=1x+14\]
Now, we will subtract \[x\] from both the sides of the equality in the above equation, we have,
\[\Rightarrow 3x-1x=1x+14-1x\]
We get on solving,
\[\Rightarrow 3x-1x=14\]
We have separated the \[x\] terms and the constants, so we now have to find the value of \[x\].
\[\Rightarrow 2x=14\]
\[\Rightarrow x=\dfrac{14}{2}\]
\[\Rightarrow x=7\]
Therefore, the value of \[x=7\].

Note:
We can check if the value of \[x\], we got is correct or not, we will simply put the value of \[x\] in the expression given to us and prove that LHS = RHS.
The expression we have,
\[3x+5=1x+19\]
Taking LHS, we get,
\[3x+5\]
Substituting the value of \[x=7\], we get,
\[\Rightarrow 3(7)+5\]
\[\Rightarrow 21+5\]
\[\Rightarrow 26\]
Taking RHS, we get,
\[1x+19\]
Substituting the value of \[x=7\], we get,
\[\Rightarrow 1(7)+19\]
\[\Rightarrow 7+19\]
\[\Rightarrow 26\]
Since, LHS = RHS,
Therefore, the value of \[x=7\].