Checking a Solution by Substitution

≈ 20 min

A value is a solution of an equation if substituting it for the variable makes both sides equal. Checking is a two-step routine:

Substitute the value into the left-hand side (LHS) and right-hand side (RHS) separately.
Compare: if LHS $=$ RHS, the value is a solution.

Worked example. Is $x = 4$ a solution of $2x - 3 = 5$ ?

\text{LHS} = 2(4) - 3 = 8 - 3 = 5 \qquad \text{RHS} = 5

LHS $=$ RHS, so yes, $x = 4$ is a solution.

Is $x = 4$ a solution of $2x - 3 = 5$ ?

Yes — both sides equal 5

No — the left side equals 11

No — the left side equals 3

Cannot tell without solving

Which value of $x$ satisfies $3x + 1 = 10$ ?

$x = 2$

$x = 3$

$x = 4$

$x = 9$

What value of $x$ makes $\dfrac{x}{2} = 6$ true?