Pre-Algebra A Midterm Review

Front

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

Back

An equation has no solutions when there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

Front

How do you simplify the equation 3x - 8 = 3(x - 4) + 1?

Back

When simplified, both sides lead to a contradiction, indicating that the equation has no solutions.

Front

What is the solution to the inequality 3(x - 2) < 2(x + 9)?

Back

The solution is x < 24.

Front

What is slope-intercept form of a linear equation?

Back

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the equation 5x - 3y = -9 to slope-intercept form.

Back

The slope-intercept form is y = (5/3)x + 3.

Front

What does the inequality 14 < -2a + 6 - 2a represent?

Back

It represents the condition a < -2.

Front

How do you write an equation for a situation involving multiple items with different prices?

Back

You can represent the total cost with an equation like 15x + 20y = 150, where x and y are the quantities of each item.

Front

What is the first step in solving the equation 3x - 8 = 3(x - 4) + 1?

Back

Distribute the 3 on the right side: 3x - 8 = 3x - 12 + 1.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation, often resulting in an identity.

Front

What is the process to solve the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute and combine like terms to isolate x, leading to the solution x < 24.