4. Equations with No Solutions or Infinitely Many Solutions - 2. Analyze and Solve Linear Equations

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

No solution

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using inverse operations. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

3(2.4x+4)=4.1x+7+3.1x

Distribute 3

7.2x+12=4.1x+7+3.1x

Now, we can continue to solve using inverse operations.

7.2x+12=4.1x+7+3.1x

LHS-7.2x=RHS-7.2x

7.2x+12-7.2x=4.1x+7+3.1x-7.2x

Commutative Property of Addition

7.2x-7.2x+12=4.1x+3.1x-7.2x+7