Question

Explain how you know the equation x+1=4 is equivalent to the equation 4x+8=20

Answer 1

Equivalent equations are algebraic equations that have identical solutions or roots.

To check the equivalency of both equations, we can solve both equations to check the solutions.

Equation 1: x + 1 = 4

`\begin{gathered} x+1=4 \\ x=4-1 \\ x=3 \end{gathered}`

Equation 2: 4x + 8 = 20

`\begin{gathered} 4x+8=20 \\ 4x=20-8 \\ 4x=12 \\ x=(12)/(4) \\ x=3 \end{gathered}`

Since the solution of both equations is x = 3, this means that both equations are equivalent.