Welcome to Algebra I
These lessons build from solving and graphing linear equations to systems, polynomials, factoring and quadratics, then radicals and rational expressions. Open each example and use the practice sets to go at your own pace.
2. Distribute and combine like terms before isolating $x$
3. Variables on both sides — gather $x$ on one side
4. Linear inequalities and the “flip the sign” rule
An equation says two expressions are equal. To solve, find every value of the variable that makes the equation true.
Balance rule: add, subtract, multiply, or divide both sides by the same nonzero number (when dividing). You are “undoing” what was done to $x$.
Inequalities ($<$, $>$, $\le$, $\ge$) work the same way—except if you multiply or divide both sides by a negative number, you must reverse the inequality symbol.
Simplify each side (distribute, combine like terms), then move variable terms to one side and constants to the other. Finish by dividing to get $x=\ldots$ (or an inequality for $x$).
1. Solve linear equations
Why learn this?
Models everywhere. Rates, totals, and constraints in science and finance often boil down to “find $x$ so this equation is true.”
Helpful hints
Undo in reverse order. If $x$ was multiplied then something was added, undo the addition first, then divide.
Remember
Same operation on both sides · Check by substituting your answer into the original equation.
2. Distribute & combine
Why learn this?
Clear the parentheses first. Distributing turns $a(x+b)$ into $ax+ab$ so you can combine like terms on each side.
Helpful hints
Watch signs. $-(x-2)=-x+2$. Combine all $x$ terms, then all constants, before isolating $x$.
Remember
$a(b+c)=ab+ac$ · Simplify each side before you “move” terms across $=$.
3. Variables on both sides
Why learn this?
Both sides can have $x$. Gather every $x$ term on one side and constants on the other, then solve the simpler equation.
Helpful hints
Subtract the smaller $x$ pile. Subtracting $4x$ from both sides of $5x=4x+7$ leaves $x$ on one side only.
Remember
Combine like terms on each side first · Balance every move.
4. Linear inequalities
Why learn this?
“At most” and “at least.” Budgets, speeds, and tolerances are often inequalities, not single values.
Helpful hints
Flip when multiplying by a negative. If you divide or multiply both sides by a negative number, reverse $\lt$ and $\gt$ (and $\le$ / $\ge$).
Remember
Open dot vs. closed dot on graphs (later) · Solution sets can be intervals, not just one number.