Solveeit Logo

Question

Question: How do you solve \(3x - 10 = 5x + 8\)?...

How do you solve 3x10=5x+83x - 10 = 5x + 8?

Explanation

Solution

In order to determine the value of variablexx in the above equation use the rules of transposing terms to transpose terms having (x)(x)on the Left-hand side and constant value terms on the Right-Hand side of the equation. Solving like terms and dividing both sides of the equation with the coefficient of xxwill lead to your required result.

Complete step by step solution:
We are given a linear equation in one variable 3x10=5x+83x - 10 = 5x + 8.and we have to solve this equation for variable (xx).
3x10=5x+8\Rightarrow 3x - 10 = 5x + 8

Now combining like terms on both of the sides. Terms having xx will on the Left-Hand side of the equation and constant terms on the right-hand side .

Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term get reversed .In our case,10 - 10 will become +10 + 10on RHS and 5x5x in LHS will become 5x - 5x in LHS

After transposing terms our equation becomes
3x5x=10+8 2x=18  \Rightarrow 3x - 5x = 10 + 8 \\\ \Rightarrow - 2x = 18 \\\

Now dividing both sides by the number 2 - 2

2x2=182 x=9 \Rightarrow \dfrac{{ - 2x}}{{ - 2}} = \dfrac{{18}}{{ - 2}} \\\ \Rightarrow x = - 9 \\\

Therefore, the solution to the equation 3x10=5x+83x - 10 = 5x + 8is equal to x=9x = - 9.

Note: Linear Equation: A linear equation is a equation which can be represented in the form of ax+cax + cwhere xxis the unknown variable and a,c are the numbers known where a0a \ne 0.If a=0a = 0then the equation will become a constant value and will no longer be a linear equation .