What is the solution to the equation $$\frac{x}{2} = 5$$ ?

To solve for x, multiply both sides by 2: $$x = 10$$ .

How do you solve the equation $$\text{log}_8(x) + \text{log}_8(x+2) = 1$$ ?

Use the property of logarithms: $$\text{log}_b(m) + \text{log}_b(n) = \text{log}_b(mn)$$ . This gives $$\text{log}_8(x(x+2)) = 1$$ , leading to $$x(x+2) = 8$$ .

What is the first step in solving the equation $$2x + 3 = 11$$ ?

Subtract 3 from both sides: $$2x = 8$$ .

What is the solution to the equation $$x^2 - 4 = 0$$ ?

Factor the equation: $$(x - 2)(x + 2) = 0$$ , giving solutions $$x = 2$$ and $$x = -2$$ .

How do you check if your solution to an equation is correct?

Substitute the solution back into the original equation to see if both sides are equal.

What is the significance of the discriminant in a quadratic equation?

The discriminant, $$b^2 - 4ac$$ , determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

What does it mean for an equation to be linear?

A linear equation is an equation of the first degree, meaning it can be written in the form $$ax + b = 0$$ , where a and b are constants.

What is the solution to the equation $$3x - 9 = 0$$ ?

Add 9 to both sides and then divide by 3: $$x = 3$$ .

What is the graphical representation of a linear equation?

The graphical representation of a linear equation is a straight line on a coordinate plane.

What is the purpose of isolating the variable in an equation?

Isolating the variable helps to simplify the equation and makes it easier to find the value of the variable.

Solve Equations using Desmos Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the purpose of using Desmos in solving equations?

Back

Desmos is an online graphing calculator that helps visualize equations and inequalities, making it easier to understand their behavior and find solutions.

2.

FLASHCARD QUESTION

Front

Define a logarithm in the context of solving equations.

Back

Tags

CCSS.HSF.BF.B.5

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.6.EE.B.7

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is the quadratic formula used for?

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What does it mean to 'solve for x'?

Back

To 'solve for x' means to find the value(s) of x that make the equation true.

Tags

CCSS.7.EE.B.4A

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.7.EE.B.4A

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