Isolate x in one-step equations by applying the same operation to both sides, including adding, subtracting, multiplying, or dividing, and verify with substitution, including negative numbers.

Learn to solve multi-step equations by isolating x, moving terms to one side, and applying addition, subtraction, multiplication, and division through step-by-step examples and practice.

learn to solve proportions using cross multiplication, work with ratios like 2/3 = x/9, and simplify through division.

Section 3 introduces more complex content; watch the videos multiple times and practice plenty of questions to master these sections.

discover how to find the slope of a line from two points using the formula (y2−y1)/(x2−x1), with rise over run, including zero slope and undefined cases.

Explore the slope-intercept form y=mx+b for linear functions, identifying slope m and y-intercept b from examples, and practice plotting lines using rise over run.

Explore how to work with linear equations in standard form by finding the x- and y-intercepts, converting to slope-intercept form, and interpreting the slope and intercepts through worked examples.

Determine a line from two points with the slope formula m = (y2 - y1)/(x2 - x1) and the point-slope form y - y1 = m(x - x1).

determine the equation of lines parallel to a given line through a point by applying the point-slope form, using the same slope for parallels, and converting to slope-intercept form.

Determine equations of lines perpendicular to a given line by using negative reciprocals of slopes and the point-slope form. Practice through examples to find equations through specific points.

Explore solving one-step inequalities using addition or subtraction, and multiplication or division by a negative number, with a number line and appropriate inequality flips.

Master multistep inequalities by isolating the variable, using addition and subtraction, and applying sign flips when multiplying or dividing by negatives, with number line visuals showing closed or open dots.

Learn to solve compound inequalities by splitting or combining, using number lines to show the solution set, and applying and (intersection) or (union) rules with inclusive or exclusive endpoints.

Expand polynomial expressions by applying foil—multiply the first, outside, inside, and last terms. Then simplify by combining like terms and ordering results in descending powers of x.

Learn to factor trinomials by finding two numbers that multiply to the constant and sum to the middle term, building binomials like x-4 and x+7 through practice.

Factor trinomials by splitting the middle term and using grouping. Find two numbers that multiply to ac and add to b, as shown in examples like ac=6 and b=7 (6 and 1).

Learn to factor differences of two squares using a squared minus b squared equals (a plus b)(a minus b), with examples like x squared minus 1.

Identify the vertex coordinates of quadratic graphs using the standard form y = a(x - h)^2 + k, and understand how h and k locate the vertex.

Graph quadratic functions by starting with the standard parabola y = x^2, locating the vertex, and translating to the vertex form y = a(x − h)^2 + k to plot symmetric shapes, as in y = x^2 − 1.

Learn how to find the vertex of a quadratic in general form by completing the square, and see how coefficients shift and shape the parabola.

Learn how to find the vertex of a quadratic in general form by completing the square, turning it into a perfect square trinomial, and reading the vertex from the expression.

Learn to solve equations by completing the square, balance the addition, form a perfect square, take square roots with plus/minus, and find solutions such as x = -1 or -3.

Learn to solve equations with the quadratic formula by plugging a, b, and c into (-b ± sqrt(b^2-4ac))/(2a) to find one or two roots.

Review prime number factorization by dividing by the smallest prime factor, showing 12 = 2^2 × 3 and 18 = 2 × 3^2, with divisibility checks.

Learn to simplify radicals by prime factorization of numbers inside the square root, extract pairs as outside factors, and rewrite using perfect squares to clarify the process.

Explore adding and subtracting radicals by combining like terms. Recognize when terms share the same radical and simplify through factoring out perfect squares, keeping remaining radicals.

Master multiplying and simplifying radicals by multiplying outside numbers and inside radicands, with examples like sqrt(5) times sqrt(2) equals sqrt(10) and sqrt(3) times sqrt(2) equals sqrt(6).

Learn how to rationalize denominators with radicals by multiplying by conjugates, simplifying radicals, and using distributive steps through worked examples.

Solve radical equations by squaring both sides and verifying solutions, illustrated with examples using square roots, checking candidate x values, and confirming results.

Learn how to solve radical equations by isolating the square root, squaring both sides, and simplifying or factoring to find solutions, with checks for extraneous roots.

Learn to simplify rational expressions by factoring and canceling factors in products, and understand why cancellation does not apply to addition or subtraction.

Explore multiplying and dividing rational expressions by factoring and canceling common factors. Learn to simplify by canceling top and bottom, and remember to change only the second fraction when dividing.

Learn how to add and subtract rational expressions by finding a common denominator and combining numerators. The lesson uses step-by-step fraction examples, including 1/2 + 1/3, to reinforce the method.

Learn to add and subtract rational expressions by factoring polynomials, determining a common denominator, and carefully applying signs across numerators.

Learn to solve rational equations by finding the least common denominator, cross-multiplying, canceling terms, and checking solutions across examples.

Use the least common denominator to solve rational equations by multiplying through by x, simplifying, and checking non-permissible values; find x = -3/2 and x = 2.

Solve systems by graphing to find the intersection as the solution, using slope and y-intercept concepts; recognize parallel lines with no solution and identical slopes with infinite solutions.

Learn to solve systems by elimination by adding or subtracting equations to eliminate a variable, then solve for the other variable and express the solution as coordinate pairs.

Eliminate variables in systems by creating matching coefficients, multiplying equations, and solving for x and y; identify cases with unique solutions, no solution (parallel lines), or infinite solutions.

Learn to solve systems by substitution by isolating y, substituting into the second equation, solving for x, and then finding y from x.

Graph and solve systems of linear inequalities by shading the feasible region bounded by lines. Use solid lines for non-strict inequalities and dotted lines for strict ones.

Learn to solve simple algebra word problems by setting up two-number equations with given sum and difference, using x for the first number, solving, and verifying results.

Translate simple algebra word problems into equations with two numbers, set up relationships such as sums, differences, and multiples, solve for the numbers, and verify the solutions.

Solve mixture problems by converting percentages to decimals, forming equations with total gallons, and solving for component amounts, as shown with 20%/80% nectar and 25%/75% cocoa blends.

Solve mixture problems with concentration equations: 12 oz of 80% grape juice to 30% needs 20 oz orange juice; 4 gal of 20% alcohol to 8% needs 6 gal water.

Apply uniform motion to riders moving in opposite directions at 30 mph and 24 mph to find when they are 260 miles apart; using relative speed, it takes four hours.

Solve a uniform motion catch-up problem with two travelers moving north at 40 mph and 50 mph, one hour apart, to find when Pegasus catches up.

Learn to solve consecutive integer and consecutive odd integer word problems by setting x as the first term and forming equations from sums like 100, 76, and 75.