Question

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$5 x-1=3+x$$

Short answer

The given mathematical notation, \(5x - 1 = 3 + x\), is an equation.

Step-by-step solution

Identify the given problem

The given problem is an algebraic notation: \[5x - 1 = 3 + x\]. Here, as one can see, two expressions (5x - 1 and 3 + x) are compared to each other with an 'equals' sign

Determine if the problem is Equation or Inequality

As per the definitions, if the given problem were an inequality, it would have a 'greater than', 'less than', 'greater than or equal to', or 'less than or equal to' sign instead of an 'equals' sign. So, since the problem is having an 'equals' sign, we can conclude that the given mathematical notation is not an inequality.

Final Evaluation

From Steps 1 and 2, it is found that the given problem has the characteristics of an equation as it comprises two expressions compared with the 'equals' sign and it is not an inequality. Therefore, the given problem \[5x - 1 = 3 + x\] is an equation.