\section*{Algebra Practice Worksheet: Equations & Inequalities}

Practice solving various types of algebraic equations and inequalities with this comprehensive worksheet. Includes step-by-step solutions and explanations.

\subsection*{Linear Equations}

\subsubsection*{Problem 1} Solve for $x$: $3x + 7 = 22$

\textbf{Solution:} \begin{align*} 3x + 7 &= 22 \ 3x &= 22 - 7 \ 3x &= 15 \ x &= 5 \end{align*}

\subsubsection*{Problem 2} Solve for $x$: $2(x - 3) = 4x + 6$

\textbf{Solution:} \begin{align*} 2(x - 3) &= 4x + 6 \ 2x - 6 &= 4x + 6 \ 2x - 4x &= 6 + 6 \ -2x &= 12 \ x &= -6 \end{align*}

\subsection*{Quadratic Equations}

\subsubsection*{Problem 3} Solve: $x^2 - 5x + 6 = 0$

\textbf{Solution:} Using factoring: $x^2 - 5x + 6 = (x - 2)(x - 3) = 0$ Therefore, $x = 2$ or $x = 3$

\subsubsection*{Problem 4} Solve: $2x^2 + 7x - 4 = 0$

\textbf{Solution:} Using quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ \begin{align*} x &= \frac{-7 \pm \sqrt{49 - 4(2)(-4)}}{4} \ x &= \frac{-7 \pm \sqrt{81}}{4} \ x &= \frac{-7 \pm 9}{4} \ x &= \frac{1}{2} \text{ or } x = -4 \end{align*}

\subsection*{Systems of Equations}

\subsubsection*{Problem 5} Solve the system: \begin{align*} 2x + y &= 8 \ x - y &= 1 \end{align*}

\textbf{Solution:} Adding the equations: $3x = 9$, so $x = 3$ Substituting: $3 - y = 1$, so $y = 2$ Answer: $x = 3$, $y = 2$

\subsection*{Keywords} algebra practice, linear equations, quadratic equations, systems of equations

\subsection*{Last Updated} July 12, 2025, 05:38 PM +04