Front

What is the result of simplifying the expression: (5x + x^2 - 4) - (4x - x^2 + 6)?

Back

The result is: 2x^2 + x - 10.

Front

Simplify the expression: 8x + 3(2x - 5) - x.

Back

The simplified expression is: 8x + 6x - 15 - x.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What does it mean for a point to be a solution of a linear inequality?

Back

A point is a solution of a linear inequality if it makes the inequality true when substituted into the inequality.

Front

Identify the solution set for the inequality: y > -1/4x - 1.

Back

The solution set includes all points above the line y = -1/4x - 1.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a relationship of greater than or less than (e.g., y < mx + b).

Front

What is the solution set for the inequality x - 4y > 4?

Back

The solution set includes all points above the line x - 4y = 4.

Front

How do you determine if a point is part of the solution set for an inequality?

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the significance of the point (4, -2) in relation to the inequality x - 4y > 4?

Back

The point (4, -2) satisfies the inequality, meaning it is part of the solution set.