Question

Solve \[2x - 10 = - 3x\]?

Answer 1

Hint: The equation is an algebraic equation, where the algebraic equation is the combination of constants and variables. To solve the above algebraic equation, we use the tables of multiplication and we can find the value of $x$.

Complete step by step solution:
The algebraic expression is an expression which consists of variables and is consistent with the arithmetic operations. The above equation is a linear equation where the linear equation is defined as the equations are of the first order. These equations are defined for lines in the coordinate system. To solve this linear equation, we apply simple methods. Since by solving these types of equations we get only one value.
Now we solve the given equation, let us consider the equation
\[2x - 10 = - 3x\]
Take 2 as common in the LHS we have
\[ \Rightarrow 2(x - 5) = - 3x\]
Now divide the equation by 2 we get
\[ \Rightarrow x - 5 = - \dfrac{3}{2}x\]
Take \[ - \dfrac{3}{2}x\] to the LHS and $-5$ to RHS we get
\[ \Rightarrow x + \dfrac{{3x}}{2} = 5\]
\[ \Rightarrow \dfrac{{5x}}{2} = 5\]
On cancelling 5 on both sides we get
\[ \Rightarrow \dfrac{x}{2} = 1\]
\[ \Rightarrow x = 2\]
Therefore, the value of $x$ is equal to $2$.

Note:
We can also solve this by another method. Now consider the equation
\[2x - 5 = - 3x\]
Take -3x to the LHS and -5 to the RHS we get
\[ \Rightarrow 2x + 3x = 10\]
On simplifying we get
\[ \Rightarrow 5x = 10\]
On dividing by 5 we get
\[ \Rightarrow x = 2\]
Therefore, we have \[x = 2\]
Hence we have solved the given equation
Therefore, the value of x is \[x = 2\].
If we solve the equation by the different methods the result obtained will be the same.

The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the tables of multiplication, we can solve the equation.