Introduction to equations

What makes an equation, true and false equations, solutions, and solving simple equations by inspection or guess and check.

What is an equation?

An equation has an equals sign: $2x + 1 = 9$. An expression does not: $2x + 1$. A solution is a value that makes the equation true.

Example 1●

Is $x = 4$ a solution of $2x + 1 = 9$?

Left side: $2(4) + 1 = 9$. Right side: $9$.

Both sides are equal, so yes.

For simple equations, ask "what number makes this true?"

Example 2●

Solve (a) $x + 7 = 12$, (b) $5m = 35$, (c) $\dfrac{k}{3} = 6$.

(a) $x = 5$ (b) $m = 7$ (c) $k = 18$

Flashcards

Equation

A statement that two expressions are equal (has $=$).

Solution

A value that makes the equation true.

Solve $4a = 28$

$a = 7$

Practice