MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

MathLabwith Mr. Ahmed
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1.5 Equations

Focus on solve an equation and quadratic equation.

Before you solve

Ideas in this lesson

Review the ideas below. Select one to see worked steps and five practice questions.

01Is it a solution?Worked steps · five questions02Linear equationsWorked steps · five questions03Solving for a variableWorked steps · five questions04Solving quadratics by factoringWorked steps · five questions05Completing the squareWorked steps · five questions06The quadratic formulaWorked steps · five questions07The discriminantWorked steps · five questions08Rational and radical equationsWorked steps · five questions09Quadratic-type, power and absolute value equationsWorked steps · five questions10Applications of supplied equationsWorked steps · five questions
Lesson brief and rules

1.5 Equations

Apply equal operations to both sides and check solutions in the original equation.

Worked example 11
01 / A student tests 22 and 55 in (x−2)(x−5)x−2=0\dfrac{(x-2)(x-5)}{x-2}=0. Which is the solution set?
02 / The denominator requires x≠2x\ne 2.
03 / For an allowed input the fraction simplifies to x−5x-5.
04 / The only possible zero is x=5x=5, which is permitted.
05 / The value 22 is not a solution because the original expression is undefined.
Worked example 2 · Is it a solution?

To solve x+5=3\sqrt{x+5}=3 a student squares both sides. Which conclusion is justified?

The square root must equal the nonnegative number 33.
x+5=9x+5=9 follows on squaring.
Subtract 55 to obtain x=4x=4.
Substitution gives 9=3\sqrt{9}=3, so the candidate is valid.

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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