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How can reverse operations be used to solve an equation such as 2x + 7 = 19?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — algebra This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

To solve the equation $2 x + 7 = 19$ , you use inverse operations to isolate the variable $x$ . An inverse operation is a mathematical procedure that undoes the effect of another operation.12

Follow these steps to solve the equation:

Undo Addition: The equation adds 7 to the term containing $x$ . To reverse this, subtract 7 from both sides of the equation:
$2 x + 7 - 7 = 19 - 7$
$2 x = 12$
Undo Multiplication: The variable $x$ is currently multiplied by 2. To reverse this, divide both sides by 2:
$\frac{2 x}{2} = \frac{12}{2}$
$x = 6$

By applying these inverse procedures, you effectively "undo" the operations performed on $x$ , allowing you to determine its value. This principle of inversion is fundamental to solving equations in mathematics.1