Question

How do you solve the linear equation \[\dfrac{x}{8}-5=-1\]?

Answer 1

Hint: This type of problem is based on the concept of solving linear equations with one variable. Here, the variable is x. First, we have to add 5 on both the sides of the given equation. Then, simplify the equation in such a way that the variable is in the left-hand side and the constant is in the right-hand side. And then multiply the whole obtained equation by 8 to get the value of x which is the required answer.

Complete step-by-step solution:
According to the question, we are asked to solve \[\dfrac{x}{8}-5=-1\].
We have been given the equation is \[\dfrac{x}{8}-5=-1\]. ---------(1)
We have to first convert the left-hand side of the equation to variable x and the right-hand side to a constant.
Let us first add 5 on both the sides of the equation.
\[\dfrac{x}{8}-5+5=-1+5\]
We know that terms with the same magnitude and opposite sign cancel out.
Therefore, \[\dfrac{x}{8}=-1+5\].
On further simplification, we get
\[\dfrac{x}{8}=4\]
Now, multiply the whole obtained equation by 8. We get
\[\dfrac{x}{8}\times 8=4\times 8\]
Here, the common term 8 cancels out the numerator and denominator of the LHS.
We get \[x=4\times 8\].
On further simplification, we get
\[x=32\]
Therefore, the value of x in the equation \[\dfrac{x}{8}-5=-1\] is 32.

Note:We should make necessary calculations in the given equation to obtain the value of x which is the required answer. Also avoid calculation mistakes based on sign conventions. We can also solve this problem by multiplying the whole given equation by 8 and then solve the rest of the question. Since the given equation is linear, we get only one value for x.