Flashcard 6 2024 Equation Variables on both sides, no & infinite soln

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, meaning both sides of the equation are equivalent for all values.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation, meaning both sides of the equation are never equal.

Front

Solve: -3(-2x - 5) + 2x - 8 = 2(2x + 3) + 4x + 1

Back

Infinite solutions

Front

Solve: 10x - 22 = 5(2x + 11)

Back

No Solution

Front

Solve: 11a + 9(a + 2) = 6(2a + 9)

Back

a = 4.5

Front

Solve: 8m + 12 = 4(2m + 3)

Back

Infinite Solutions

Front

Solve: 4 + 2(4x - 1) = 6x - 14

Back

x = -8

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to simplify both sides of the equation, often by combining like terms.