Solve each equation or inequality. | 7 + 2x| = 0

Verified step by step guidance

1. Identify the absolute value equation: \(|7 + 2x| = 0\).
2. Recall that the absolute value of a number is zero only if the number itself is zero.
3. Set the expression inside the absolute value equal to zero: \(7 + 2x = 0\).
4. Solve for \(x\) by isolating \(x\): subtract 7 from both sides to get \(2x = -7\).
5. Divide both sides by 2 to solve for \(x\): \(x = -\frac{7}{2}\).

Key Concepts

Absolute Value

Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number 'a', the absolute value is defined as |a| = a if a ≥ 0, and |a| = -a if a < 0. In the context of equations, setting an absolute value expression equal to zero indicates that the expression inside must also equal zero.

Solving Equations

Solving equations involves finding the values of variables that make the equation true. In this case, we need to isolate the variable 'x' by manipulating the equation. Understanding how to perform operations such as addition, subtraction, multiplication, and division is essential for solving equations effectively.

Zero Property of Absolute Value

The zero property of absolute value states that the only time an absolute value expression equals zero is when the expression inside the absolute value is also zero. This means that for |A| = 0, A must equal 0. This property is crucial for determining the solutions to equations involving absolute values.