Solving one variable linear equations

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What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when the equation simplifies to a false statement, such as 0 = 5.

Tags

CCSS.8.EE.C.7A

Front

How do you solve a linear equation with one variable?

Back

To solve a linear equation with one variable, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Tags

CCSS.7.EE.B.4A

Front

What is the significance of the equation 2x + 1 = 2x - 1?

Back

This equation has no solution because when simplified, it leads to the false statement 1 = -1, indicating that there are no values of x that can satisfy the equation.

Tags

CCSS.8.EE.C.7A

Front

What is the first step in solving the equation -4(3w + 4) - 14 = 3(2w - 4) - 9w?

Back

The first step is to distribute the -4 and 3 across their respective parentheses to simplify the equation.

Front

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

Back

Isolating a variable means rearranging the equation so that the variable is on one side by itself, allowing you to find its value.

Tags

CCSS.6.EE.B.7

Front

What is the solution to the equation w = -2?

Back

The solution indicates that the value of the variable w is -2, which satisfies the equation when substituted back.

Front

What is the process of checking a solution in a linear equation?

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To check a solution, substitute the value of the variable back into the original equation to see if both sides are equal.

Front

What is the result of solving the equation 1/2(4x - 8) = 1/4(8x + 12)?

Back

The result is that there are no solutions, as the equation simplifies to a false statement.

Tags

CCSS.8.EE.C.7A

Front

What is the importance of understanding the concept of 'no solution' in linear equations?

Back

Understanding 'no solution' helps students recognize when an equation does not have a valid answer, which is crucial for problem-solving.

Tags

CCSS.8.EE.C.7A