Solving one variable linear equations

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be expressed in the form ax + b = 0, where a and b are constants and x is the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions if any value of the variable satisfies the equation, often occurring when both sides of the equation are equivalent.

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.

Front

What is the solution to the equation 2w/5 - 9 = 11?

Back

The solution is w = 50.

Front

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

Back

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

Front

What is the significance of the equation 1/6 x = 15 in a word problem?

Back

This equation represents a relationship where one sixth of the total number of candies (x) equals 15, allowing you to find the total number of candies.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting coefficients of terms that have the same variable raised to the same power.

Front

What does it mean to have a unique solution in a linear equation?

Back

A unique solution means there is exactly one value for the variable that satisfies the equation.

Front

What is the role of constants in linear equations?

Back

Constants are fixed values that do not change and can affect the position of the line represented by the equation on a graph.