Decoding the Algebra: How to Solve '2x + 4 = 18'

Decoding the Algebra: How to Solve '2x + 4 = 18'

Solving a linear equation like $2x + 4 = 18$ is a foundational exercise in modern mathematics, representing a universal language of logic that transcends spoken tongues.

Step-by-Step Breakdown

1. Isolate the variable term: Subtract 4 from both sides of the equation to maintain balance.

$$2x + 4 - 4 = 18 - 4$$

$$2x = 14$$

1. Isolate the variable ($x$): Divide both sides by the coefficient 2.

$$\frac{2x}{2} = \frac{14}{2}$$

$$x = 7$$

The Linguistic and Historical Roots

Mathematically, the word algebra originates from the Arabic al-jabr, meaning "the reunion of broken parts," coined by the 9th-century Persian mathematician Muhammad ibn Musa al-Khwarizmi. Equations are essentially sentences written in a formal, symbolic grammar where numbers act as nouns and operators act as verbs. Solving for $x$ is the linguistic process of uncovering an unknown variable through deductive reasoning.