Unit 2.1 - 3 Solving Equations and Inequalities

Front

What is the first step to solve the equation 10x - 9 = 4x - 9?

Back

Combine like terms by moving all terms involving x to one side and constant terms to the other side.

Front

What does it mean when an equation has infinite solutions?

Back

It means that any value of the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

Front

In the equation 1 + x + 5 = 3x + 5, what is the error made in Step 3?

Back

The error is in the simplification; it should be -2x + 6 = 5, not -2x = 11.

Front

How do you represent three consecutive even numbers algebraically?

Back

Let the first even number be x, then the next two can be represented as x + 2 and x + 4.

Front

What is the equation to represent the statement 'A piece of pipe is triple the sum of a number and fourteen'?

Back

The equation is 3(x + 14) = 72.

Front

What is the solution to the equation 3x + 6 = 48?

Back

x = 14.

Front

What is the process of isolating a variable in an equation?

Back

It involves performing operations to get the variable on one side of the equation and constants on the other side.

Front

What does it mean to find the error in solving an equation?

Back

It means to identify where a mistake was made in the steps taken to arrive at the solution.

Front

What is the significance of checking your work after solving an equation?

Back

It ensures that the solution is correct and that no errors were made during the solving process.

Front

How can you verify if a solution to an equation is correct?

Back

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