Question

Solve the equation $|2 x+5|=12(p .51)$

   Solve the equation
$|2 x+5|=12(p .51)$

McDougal Littell Algebra 2

McDougal Littell Algebra 2

Holt McDougal, Ron… 9th Edition

Chapter 3, Problem 45

Instant Answer

Solved by Expert Ankit Singh

03/04/2022

Step 1

51) \] Step 2: Calculate the right side of the equation. First, simplify \(12(p \cdot 0.51)\): \[ 12 \cdot 0.51 = 6.12 \] Thus, the equation becomes: \[ |2x + 5| = 6.12 \] Step 3: Now, we need to solve the absolute value equation. This gives us two cases to Show more…

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Solve the equation $|2 x+5|=12(p .51)$

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Key Concepts

Absolute Value Function

The absolute value function outputs the non-negative magnitude of a number regardless of its sign. This concept is fundamental in solving equations where the absolute value of an algebraic expression is equated to a positive number.

Case Analysis

When solving absolute value equations, a common technique involves splitting the equation into two cases based on the definition of absolute value: one where the expression inside is equal to the given number and another where it is equal to the negative of that number. This method ensures that all possible solutions are considered.

Linear Equations

After the equation is split into cases, each case typically results in a linear equation. Solving these linear equations involves isolating the variable using standard algebraic operations, which is a key process in finding the final solutions.

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