Question

How do you solve \[3\left( g-1 \right)-7=3g+4\]?

Answer 1

Hint: We have to use the distributive property to solve this question, the property is as \[a\left( b+c \right)=ab+ac\]. The degree of an equation is the highest power to which the variable in the equation is raised. If the degree of the equation is one, then it is a linear equation. To solve a linear equation, we have to take all the variable terms to one side of the equation, and leave constants to the other side. By this, we can find the solution value of the equation.

Complete step by step solution:
We are given the equation \[3\left( g-1 \right)-7=3g+4\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[3\left( g-1 \right)-7=3g+4\]
Simplifying the above expression using the distributive property, we get
\[\Rightarrow 3g-3-7=3g+4\]
Subtracting \[3g\] from both sides of above expression, we get
\[\Rightarrow -10=4\]
But this statement is false.
Hence, the given equation has no solution.

Note: We can solve these types of questions without separating the variable and constant terms. Here, as we can see that the coefficient of variable term on both sides of the equation is same, we get no solution. Hence, if for a given linear one variable equation the coefficient of variable is same on both sides, the equation has no solution.