Alg 1. Review 5 for the Final Exam First Semester.

Front

What is the graphical representation of the inequality 2x + y < -6?

Back

To graph the inequality 2x + y < -6, first graph the line 2x + y = -6. This line will be dashed (not solid) because the inequality is strict (<). Then, shade the region below the line, which represents all the points (x, y) that satisfy the inequality.

Front

What mistake did James make in Step 2 of solving the equation?

Back

James made a mistake in Step 2 by subtracting 2x from 8, but they are not like terms. The correct approach would be to combine like terms.

Front

What is an equivalent equation to 5x - 1 = 3x + 15?

Back

An equivalent equation is 2x - 1 = 15. This can be derived by subtracting 3x from both sides and adding 1 to both sides.

Front

How do you solve the equation 5x - 1 = 3x + 15?

Back

1. Subtract 3x from both sides: 5x - 3x - 1 = 15. 2. Combine like terms: 2x - 1 = 15. 3. Add 1 to both sides: 2x = 16. 4. Divide by 2: x = 8.

Front

What does it mean for two terms to be 'like terms'?

Back

Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, but 2x and 3y are not.

Front

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

Back

Isolating a variable involves rearranging the equation to get the variable on one side and all other terms on the opposite side. This often includes using inverse operations.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dashed line indicates that the points on the line are not included (< or >).

Front

How do you determine the solution set for the inequality 2x + y < -6?

Back

To determine the solution set, graph the line 2x + y = -6 as a dashed line and shade the area below the line, which represents all the (x, y) pairs that satisfy the inequality.

Front

What is the first step in solving the equation 3x + 5 = 20?

Back

The first step is to isolate the term with the variable by subtracting 5 from both sides: 3x = 15.

Front

What is the definition of an equation?

Back

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