Simplify each inequality if needed. Then determine whether the statement is true or false. -6 < 7 + 3

Verified step by step guidance

1. First, write down the inequality clearly: \(-6 < 7 + 3\).
2. Simplify the right-hand side by adding the numbers: \$7 + 3 = 10\(, so the inequality becomes \)-6 < 10$.
3. Interpret the inequality: check if \(-6\) is less than \$10$ on the number line.
4. Since \(-6\) is indeed less than \$10$, the inequality holds true.
5. Therefore, the statement \(-6 < 7 + 3\) is true.

Key Concepts

Inequality Symbols and Their Meaning

Inequality symbols like <, >, ≤, and ≥ compare two values to show their relative size. The symbol '<' means 'less than,' indicating the value on the left is smaller than the value on the right. Understanding these symbols is essential to interpret and solve inequalities correctly.

Simplifying Inequalities

Simplifying inequalities involves performing algebraic operations such as addition, subtraction, multiplication, or division on both sides to isolate variables or constants. This process helps clarify the inequality and makes it easier to determine its truth value.

Evaluating the Truth of an Inequality

To determine if an inequality is true or false, substitute or simplify both sides and compare their values. If the relationship holds as stated, the inequality is true; otherwise, it is false. This step is crucial for verifying solutions or statements involving inequalities.