1Cademy - Solving $$-6(x + 3) = 24$$ Using the General Strategy

Learn Before

Strategy for Solving Linear Equations

Example

Solving $-6(x + 3) = 24$ Using the General Strategy

To solve the equation $-6(x + 3) = 24$ , apply the general five-step strategy for linear equations:

Step 1 — Simplify each side: Use the Distributive Property to remove the parentheses by multiplying $-6$ by each term inside: $-6 \cdot x = -6x$ and $-6 \cdot 3 = -18$ . The equation becomes:

$-6x - 18 = 24$

Both sides are now fully simplified.

Step 2 — Collect variable terms on one side: All variable terms ( $-6x$ ) already appear on the left side only, so no rearrangement is needed.

Step 3 — Collect constant terms on the other side: The constant $-18$ sits on the same side as the variable term. To move it, add $18$ to both sides using the Addition Property of Equality:

$-6x - 18 + 18 = 24 + 18$

$-6x = 42$

Step 4 — Make the coefficient of the variable equal to $1$ : Because $x$ is multiplied by $-6$ , divide both sides by $-6$ using the Division Property of Equality:

$\frac{-6x}{-6} = \frac{42}{-6}$

$x = -7$

Step 5 — Check the solution: Substitute $-7$ for $x$ in the original equation:

$-6(-7 + 3) \stackrel{?}{=} 24$

$-6(-4) \stackrel{?}{=} 24$

$24 = 24 \checkmark$

Because both sides are equal, $x = -7$ is confirmed as the correct solution. This example illustrates that not every step of the general strategy requires action — here, Step 2 was unnecessary because the variable already appeared on only one side — but following the complete strategy systematically ensures no steps are overlooked.

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Learn Before

Related

Learn After