Question

How do you solve \[-1-4c<3\]?

Answer 1

Hint: This question is from the topic of linear equations in one variable. In this question, we will find the value of c. In solving this question, we will first take the number 1 to the right side of the equation. After that, we will solve the further equation. After that, we will divide the number 4 to both sides of the equation. After solving the further question, we will get our answer.

Complete step-by-step answer:
Let us solve this question.
In this question, we will solve the equation given in the question. The given equation is: \[-1-4c<3\]. We have to find the value of c from this equation.
The equation we have to solve is:
\[-1-4c<3\]
Now, let us take the number 1 to the right side of the equation. we can write the above equation as
\[\Rightarrow -4c<3+1\]
After adding 3 and 1 in the right side of the equation, we can write the above equation as
\[\Rightarrow -4c<4\]
Now, let us divide the number 4 to both sides of the equation. We can write the above equation as
\[\Rightarrow -\dfrac{4c}{4}<\dfrac{4}{4}\]
After dividing 4 to both the side of equation, we can write the above equation as
\[\Rightarrow -c<1\]
Now, let us take c to the right side of equation and take 1 to the left side of equation. We can write the above equation as
\[\Rightarrow -1 < c \]
The above equation can also be written as
\[\Rightarrow c>-1\]
Now, we have solved the equation \[-1-4c<3\], we get that c>-1 or we can say that the value of c is from negative of 1 to negative of infinity, where negative of 1 is excluded.

Note: We should have a better knowledge in the topic of linear equations in one variable to solve this type of question easily. Remember that, whenever we have to take a constant from left side of equation to right side of equation or vice-versa, then we will change the sign of that constant. Let us understand this from the following examples:
\[x+9=0\] can also be written as \[x=-9\]
\[x-6>0\] can also be written as \[x>6\]
\[y<-3\] can also be written as \[y+3<0\]