Solving Linear Equations - Example2

Solve for x in the following algebraic sentence 5 – 3x = 2x + 10

Solution

Given the equation 5 – 3x = 2x + 10

The like terms in the equation 5 – 3x = 2x + 10 are -3x and 2x; 5 and 10

Thus, we say bring like terms together as follows

5 – 3x = 2x + 10 (original equation)

5 - 10 = 2x + 3x (bringing like terms together)

-5 = 5x

Coefficient of x is 5.

Divide both sides by 5 as follows

 ^-5/₅ = ^5x/₅

-1 = x, which gives x = -1

Check for correctness

The given equation is 5 – 3x = 2x + 10

LHS =   5 – 3x

     =   5 – 3(-1)

     =   5 + 3

     =   8

RHS =   2x + 10

     =   2(-1) + 10

     =   -2 + 10

     =   10 – 2

     =   8 (Same as LHS)