Question

Solve and check \[2x-(3x-4)=3x-5\].

Answer 1

Hint: We will use the concept of linear equations in a single variable to solve this expression. We will isolate the variable x and then solve the equation to get the answer. And then we will substitute the value of x in the given expression to verify the answer.

Complete step-by-step answer:
Before proceeding with the question we should understand the concept of linear equations in one variable.
The linear equation in one variable is an equation that can be written in the form \[ax+b=c\], where x is a variable and a, b, c are real numbers and \[a\ne 0\]. Linear equations are also first-degree equations because the exponent on the variable is understood to be 1.
For solving an equation having only one variable, the following steps are followed
Step 1: Using LCM, clear the fractions if any.
Step 2: Simplify both sides of the equation.
Step 3: Isolate the variable.
Step 4: Verify your answer.
We see from the given equation in the question that there is no fraction so no need for step 1 we will directly move to step 2.
\[2x-(3x-4)=3x-5.........(1)\]
Now simplifying equation (1) as per step 2 we get,
\[-x+4=3x-5.........(2)\]
Now isolating x in equation (2) by moving all the variables to one side and all the numbers to another side as per step 3 we get,
\[3x+x=4+5.........(3)\]
Now solving for x in equation (3) we get,
\[4x=9\Rightarrow x=\dfrac{9}{4}\]
Now as per step 4 we verify our answer by substituting \[x=\dfrac{9}{4}\] in equation (1) and then check if the left hand side of the equation is equal to the right hand side of the equation or not. So we get,
\[\begin{align}
  & \,\Rightarrow 2\times \dfrac{9}{4}-\left( 3\times \dfrac{9}{4}-4 \right)=3\times \dfrac{9}{4}-5 \\
 & \,\Rightarrow \dfrac{9}{2}-\left( \dfrac{27-16}{4} \right)=\dfrac{27-20}{4} \\
 & \,\Rightarrow \dfrac{9}{2}-\dfrac{11}{4}=\dfrac{7}{4} \\
 & \,\Rightarrow \dfrac{18-11}{4}=\dfrac{7}{4} \\
 & \,\Rightarrow \dfrac{7}{4}=\dfrac{7}{4} \\
\end{align}\]
Hence our answer is verified.

Note: Here we have to remember the steps mentioned above to solve this question. We can make a mistake in a hurry in solving equation (2) as we may instead of adding 3x and x we may subtract these and hence we will get the wrong answer. Hence we need to take care of basic calculation mistakes while solving.