Question

How do you solve 1.4x+3.8=0.6x-0.68?

Answer 1

Hint: This type of problem is based on the concept of linear equations with one variable. First, we have to consider the whole equation and subtract 0.6x from both the sides of the equation. Then, we need to subtract 3.8 from both the sides of the equation. Do necessary calculations so that we get the variable in the LHS and the constant in the RHS. Divide the whole equation by 0.8. And, then find the value of x by cancelling the common terms and simplifying.

Complete step by step solution:
According to the question, we are asked to solve the equation 1.4x+3.8=0.6x-0.68.
We have been given the inequality is 1.4x+3.8=0.6x-0.68. -----(1)
We first have to consider equation (1).
Subtract the whole equation by 0.6x.
\[\Rightarrow 1.4x+3.8-0.6x=0.6x-0.68-0.6x\]
We know that terms with the same magnitude and opposite signs cancel out.
Therefore, on cancelling 0.6x from the RHS, we get
\[1.4x+3.8-0.6x=-0.68\]
Now, let us group the x terms and add them.
\[\Rightarrow \left( 1.4-0.6 \right)x+3.8=-0.68\]
On further simplification, we get
\[0.8x+3.8=-0.68\]
Now, we have to subtract 3.8 from both the sides of the equation.
\[\Rightarrow 0.8x+3.8-3.8=-0.68-3.8\]
We know that terms with the same magnitude and opposite signs cancel out.
Therefore, on cancelling 3.8 from the LHS, we get
\[0.8x=-0.68-3.8\]
\[\Rightarrow 0.8x=-\left( 0.68+3.8 \right)\]
On further simplification, we get
\[0.8x=-4.48\]
Now, let us divide the whole equation by 0.8.
We get
\[\dfrac{0.8x}{0.8}=\dfrac{-4.48}{0.8}\]
We find that 0.8 are common in both the numerator and denominator of the LHS.
On cancelling 0.8, we get
\[x=\dfrac{-4.48}{0.8}\]
Let us now, multiply 100 to both the numerator and denominator of the RHS.
\[\Rightarrow x=\dfrac{-4.48\times 100}{0.8\times 100}\]
On further simplification, we get
\[x=\dfrac{-448}{80}\]
We can express the equation as
\[x=\dfrac{-56\times 8}{8\times 10}\]
We find that 8 are common in both the numerator and denominator of the RHS. On cancelling 8, we get
\[x=\dfrac{-56}{10}\]
On converting x to a decimal number, we get
\[x=-5.6\]

Therefore, the value of x in the equation 1.4x+3.8=0.6x-0.68 is -5.6

Note: Whenever you get this type of problem, we should always try to make the necessary changes in the given equation to get the variable x in the left-hand side of the equation. And then bring all the constants to the right-hand side of the equation. We should avoid calculation mistakes based on sign conventions. We can also solve this question by multiplying 100 on both the sides of the equation so that we don’t get decimal numbers, that is
\[\left( 1.4x+3.8 \right)\times 100=\left( 0.6x-0.68 \right)\times 100\].
On further simplification, we get \[140x+380=60x-68\]. Now, solve the rest as usual.