Skill: Solve multi-step linear equations

To solve a multi-step linear equation, simplify both sides using operations that keep the equation balanced. Whatever you do to one side, do to the other side.

Example:

$$3(2x-1)+4=2x+17$$

1. Distribute $3$ across the parentheses:

$$6x-3+4=2x+17$$

2. Combine like terms on the left:

$$6x+1=2x+17$$

3. Move variable terms to one side. Subtract $2x$ from both sides:

$$4x+1=17$$

4. Move constant terms to the other side. Subtract $1$ from both sides:

$$4x=16$$

5. Divide by the coefficient of $x$:

$$x=4$$

So, the solution is $\boxed{x=4}$.

Check the solution by substituting $4$ into the original equation:

$$3(2\cdot4-1)+4=2\cdot4+17$$ $$3(8-1)+4=8+17$$ $$21+4=25$$

Since both sides equal $25$, $x=4$ is correct.

Sometimes, simplifying an equation makes the variable cancel. If a true statement remains, such as $5=5$, there are infinitely many solutions. If a false statement remains, such as $5=8$, there is no solution.