How do you solve the equation $$|y - 5| + 6 = 9$$ ?

To solve $$|y - 5| + 6 = 9$$ , first isolate the absolute value: $$|y - 5| = 3$$ . This gives two cases: 1) $$y - 5 = 3$$ (so $$y = 8$$ ) and 2) $$y - 5 = -3$$ (so $$y = 2$$ ). The solutions are $$y = 2$$ and $$y = 8$$ .

What is the process to solve the equation $$\frac{3a - 1}{4} = \frac{-2a + 4}{-2}$$ ?

To solve $$\frac{3a - 1}{4} = \frac{-2a + 4}{-2}$$ , first cross-multiply to eliminate the fractions, then simplify and solve for a. The solution is $$a = 7$$ .

How do you solve the equation $$9x - 15 = 4 + 13x - 3$$ ?

To solve $$9x - 15 = 4 + 13x - 3$$ , first simplify the right side to get $$9x - 15 = 1 + 13x$$ . Then, isolate x by moving terms involving x to one side and constant terms to the other. The solution is $$x = -4$$ .

What is the solution to the equation $$2 + 4x - 6 = 10x - 22$$ ?

To solve $$2 + 4x - 6 = 10x - 22$$ , first simplify the left side to get $$-4 + 4x = 10x - 22$$ . Then, isolate x by moving terms involving x to one side and constant terms to the other. The solution is $$x = 3$$ .

What is the distributive property?

The distributive property states that $$a(b + c) = ab + ac$$ . It allows you to multiply a single term by two or more terms inside a set of parentheses.

How do you multiply two binomials, such as $$(x + 2)(x + 3)$$ ?

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For $$(x + 2)(x + 3)$$ , the result is $$x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$ .

A binomial is a polynomial with exactly two terms. For example, $$x + 5$$ and $$3a^2 - 2b$$ are binomials.

What is the zero product property?

The zero product property states that if $$ab = 0$$ , then either $$a = 0$$ or $$b = 0$$ . This is useful for solving quadratic equations.

How do you solve a quadratic equation by factoring?

To solve a quadratic equation by factoring, express it in the form $$ax^2 + bx + c = 0$$ , then factor it into the form $$(px + q)(rx + s) = 0$$ . Set each factor to zero and solve for x.

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ , used to find the solutions of a quadratic equation $$ax^2 + bx + c = 0$$ .

What is the difference between an equation and an expression?

An equation is a mathematical statement that asserts the equality of two expressions, typically containing an equals sign (e.g., $$x + 2 = 5$$ ). An expression is a combination of numbers, variables, and operators without an equals sign (e.g., $$x + 2$$ ).

What does it mean to isolate a variable in an equation?

To isolate a variable means to manipulate the equation so that the variable is on one side of the equation by itself, allowing you to solve for its value.

Solve Equations and multiplying binomials 2022 Flashcards

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What is an absolute value equation?

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