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🔢 Algebra Essentials

Solve equations, graph lines, and crack quadratics: the core of algebra.

3
lessons
~30 min
to learn
🔢 Math
subject
Teens
level
Start the course →

What you’ll learn

  1. Solve linear equations and inequalities using balanced operations.Linear equations are solved by doing the same operation to both sides to isolate the variable. Inequalities work the same way but require flipping the sign when multiplying or dividing by a negative.
  2. Plot points, compute slope, use slope-intercept form, and solve systems.The coordinate plane locates points by ordered pairs. Slope measures steepness, y = mx + b describes lines, and systems are solved where lines intersect.
  3. Multiply and factor quadratics, apply the quadratic formula, and read the discriminant.Binomials multiply via FOIL and factor back into products. The quadratic formula solves any quadratic, the discriminant reveals the number of real solutions, and every quadratic graphs as a parabola.

Questions this course answers

Solve for x: 2x + 3 = 11.

Subtract 3 to get 2x = 8, then divide by 2 to get x = 4.

Solve: 5x - 2 = 3x + 8.

Subtract 3x and add 2 to get 2x = 10, so x = 5.

When solving -2x < 6, what happens to the inequality?

Dividing both sides by a negative flips the sign, giving x > -3.

In y = mx + b, what does b represent?

In slope-intercept form, b is the y-intercept where the line crosses the y-axis.

The solution of a two-line system is best described as:

The solution satisfies both equations, which is exactly where the lines cross.

Expand (x + 2)(x + 5).

Using FOIL: x^2 + 5x + 2x + 10 = x^2 + 7x + 10.

Grounded in trusted sources

  • The Quadratic Formula: The Discriminant, Purplemath, https://www.purplemath.com/modules/quadform3.htm
  • Discriminant, Cuemath, https://www.cuemath.com/algebra/discriminant/
  • Elementary Algebra 2e, OpenStax (Marecek et al., 2020), https://openstax.org/details/books/elementary-algebra-2e
  • Algebra, Khan Academy, https://www.khanacademy.org/math/algebra

Every Wunder lesson is built from real, reputable sources — never invented.

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