Question: Solve the equation.
7(3x + 4) = 4(3x - 1) + 23
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The solution to the equation is x = □.
1. **State the problem:** Solve the linear equation $$7(3x + 4) = 4(3x - 1) + 23$$.
2. **Apply the distributive property:** Multiply out the parentheses.
$$7 \times 3x + 7 \times 4 = 4 \times 3x - 4 \times 1 + 23$$
which simplifies to
$$21x + 28 = 12x - 4 + 23$$
3. **Combine like terms on the right side:**
$$12x - 4 + 23 = 12x + 19$$
So the equation is now
$$21x + 28 = 12x + 19$$
4. **Isolate variable terms on one side:** Subtract $$12x$$ from both sides.
$$21x + 28 - 12x = 12x + 19 - 12x$$
which is
$$\cancel{21x} + 28 - \cancel{12x} = \cancel{12x} + 19 - \cancel{12x}$$
or
$$9x + 28 = 19$$
5. **Isolate the constant term:** Subtract $$28$$ from both sides.
$$9x + 28 - 28 = 19 - 28$$
which simplifies to
$$9x = -9$$
6. **Solve for $$x$$:** Divide both sides by $$9$$.
$$\frac{9x}{\cancel{9}} = \frac{-9}{\cancel{9}}$$
which gives
$$x = -1$$
**Final answer:**
The solution to the equation is $$x = -1$$.