Mathematics
Grade9
Easy
Question
Solve the equation.Write a reason for each step.
- x = 18
- x - 12
- x = - 22
- x = - 18
Hint:
We are given an algebraic expression. We have to simplify it using algebraic rules. An algebraic expression consists of a variable and a constant. A variable doesn’t have fixed value. A constant has a fixed value.
The correct answer is: x - 12
The given expression is 5x + 2(2x -23) = -154
The first step we will do is open the bracket. We will use the distributive property for this. Distributive property states that , the quantity outside the bracket is distributed equally to the terms inside the bracket.
So, the equation becomes
5x + 2(2x -23) = -154
5x + 2(2x) – 2(23) = -154
5x + 4x – 46 = -154
Now, the above expression has four terms. Terms are the quantity that represent a single unit. It can be a variable, a constant or combination of both.
The terms which have same variables are called as like terms. The like terms are operated with each other. We can add the coefficients of the variables keeping the variable constant.
We will take the terms with variable on one side and the constants on other side
We will add 46 to both the sides.
5x + 4x – 46 + 46 = -154 + 46
5x + 4x = -108
9x = -108
Dividing both the sides by 9 we get,
x = - 12
So, the option which is “x = -12” is the right option.
For such questions, we should know about different properties of an algebraic expression. We should know the concept of like terms and unlike terms. Only like terms get added or subtracted from each other.
