Question

How do you solve \[5(3x+12)=-15\]?

Answer 1

Hint: As we can see that this question belongs to the topic linear equations of the chapter algebra. So, we should have a better knowledge in this topic. In solving this question, first we will divide both sides of the equation by 5. After that, we will subtract 12 from both sides. After that, we will divide both sides by 3. Then, we will get the value of x.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to solve the equation \[5(3x+12)=-15\]. That means we have to find the value x in this equation.
We will simplify the equation in the linear form that is x=C to get the value of x.
Let us simplify the equation.
The given equation is:
\[5(3x+12)=-15\]
After dividing by 5 in both sides of the equation, we get
\[\Rightarrow \dfrac{5\left( 3x+12 \right)}{5}=-\dfrac{15}{5}\]
\[\Rightarrow3x+12=-3 \]
Now, we will subtract 12 from both sides of the equation, we get
\[\Rightarrow 3x+12-12=-3-12 \]
\[\Rightarrow 3x=-15 \]
Now, we will divide both sides of the above equation by 3, we get
\[\Rightarrow \dfrac{3x}{3}=\dfrac{-15}{3}\]
\[\Rightarrow x=-5\]

We have solved the equation 5(3x+12)=-15 and we have got the value of x as -5.

Note: The first degree equation that we have taken in this question always has only one solution. And, we can find the value of x easily. We can cross-check if our solution is correct or not. As we have found the value of x which is -5 from the given equation \[5(3x+12)=-15. \]
Let us put the value of x in the left hand side of the equation.
So, by putting the value of x as -5 in the equation \[5(3x+12)=-15\], we get
\[5(3(-5)+12) = 5(-15+12) = 5(-3) = -15\]
As -15 is equal to the right side of the equation.
So, the left hand side of the equation is equal to the right side of the equation. So, we have solved the equation correctly and have found the correct value of x.