Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What skill is tested when solving an equation like 2x + 3 = 7?

1. Graphing

2. Algebraic manipulation and solving equations

3. Statistical analysis

4. Data interpretation

The correct answer is: Algebraic manipulation and solving equations

When solving the equation 2x + 3 = 7, the skill being tested primarily involves algebraic manipulation and the process of solving equations. In this type of problem, the objective is to isolate the variable x by performing a series of operations that maintain the equality of the equation. Initially, one needs to eliminate the constant term on the left side by subtracting 3 from both sides, leading to the equation 2x = 4. Next, by dividing both sides by 2, the solution for x can be found as x = 2. This process showcases the ability to manipulate algebraic expressions and understand the relational properties of equality. This particular skill is foundational in algebra, as it directly relates to how equations are structured and solved, laying the groundwork for more complex mathematical concepts encountered later. Other options such as graphing, statistical analysis, or data interpretation do not directly pertain to the standard problem of solving a linear equation like the one presented. These skills involve different types of processes and understanding outside of the specific context of solving for an unknown variable.