Question 1 Correct Option When You Expand The Equatio 717156

Question 1correct Optiondwhen You Expand The Equation4x 86x1210x

Identify the core assignment question: The task involves expanding and simplifying algebraic equations, then solving for the variable x. The examples include linear equations with multiple steps, such as combining like terms, isolating the variable, and performing division to find the solution.

The main instructional prompt can be summarized as: Expand the given algebraic equations, simplify, and solve for the variable.

Paper For Above instruction

Expanding and solving algebraic equations is fundamental in understanding algebraic manipulation and problem-solving. It combines knowledge of distributing, combining like terms, and rearranging equations to isolate the variable. This paper discusses techniques for expanding and solving equations, illustrating with examples similar to those provided in the assignment.

First, expanding equations involves distributing any factors across parentheses and simplifying terms. For example, in the equation 4x - 8 + 6x = 12x + 20, the first step is to combine like terms on each side. On the left side, 4x + 6x simplifies to 10x, giving 10x - 8. On the right side, 12x + 20 remains, and the goal is to isolate x.

Rearranging the equality by bringing all x terms to one side and constant terms to the other allows solving for x. Subtracting 12x from both sides results in: 10x - 12x - 8 = 20, which simplifies to -2x - 8 = 20. Adding 8 to both sides yields -2x = 28, and dividing both sides by -2 gives x = -14.

It is critical to check the solution by substituting x = -14 back into the original equation to verify correctness. This process ensures the algebraic manipulations were performed correctly and the solution is valid.

Similarly, solving more complex equations involving fractions, absolute values, or quadratic terms require specific techniques, such as multiplying through by common denominators, considering case scenarios for absolute value, or applying quadratic formula or factoring methods.

For instance, when solving equations involving absolute value, such as |x - 5| > 6, one must consider two cases: (x - 5) > 6 or (x - 5) 11 or x

In the case of equations involving exponents, roots, or trigonometric functions, specialized methods such as inverse operations, identities, or geometric interpretations might be necessary. For example, solving for angles in right triangles or using unit circle principles in trigonometry is essential for such problems.

Overall, the key to solving algebraic equations is to systematically isolate the variable through inverse operations and to carefully simplify each step. Practice with varied equations enhances understanding and problem-solving efficiency in algebra.

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