Algebra 1 Chapter 3 Eagle Test Review

Front

What does the expression \( |d-3| \ge 7 \) represent in terms of intervals?

Back

The solution is \( (-\infty, -4] \cup [10, \infty) \).

Front

When graphing an inequality, which symbols require a closed dot?

Back

The symbols are \( \leq \) and \( \geq \).

Front

What inequality does the number line graph with an open circle at -4 and a line extending left represent?

Back

The inequality is \( x < -4 \).

Front

Solve the compound inequality: -4x + 1 \( \leq \) 21 and 5x + 2 < 22.

Back

The solution is \( x \geq -5 \) and \( x < 4 \).

Front

What is the solution to the inequality -4x + 14 \( \leq \) 54?

Back

The solution is \( x \geq -10 \).

Front

Define absolute value in mathematical terms.

Back

Absolute value is the distance of a number from zero on the number line, denoted as \( |x| \).

Front

What is the graphical representation of \( x \leq 4 \)?

Back

It is represented by a closed dot at 4 and a line extending to the left.

Front

What does the symbol \( \cup \) represent in set notation?

Back

The symbol \( \cup \) represents the union of two sets.

Front

How do you solve the inequality \( 2x - 3 > 5 \)?

Back

Add 3 to both sides to get \( 2x > 8 \), then divide by 2 to find \( x > 4 \).

Front

What is the difference between \( < \) and \( \leq \)?

Back

\( < \) means 'less than' and does not include the endpoint, while \( \leq \) means 'less than or equal to' and includes the endpoint.