185 Formative 3.B Review 2020

Front

What is a compound inequality?

Back

A compound inequality is a mathematical statement that combines two or more inequalities using the words 'and' or 'or'. It describes a range of values that satisfy all the inequalities involved.

Front

How do you represent the sum of two integers in an inequality?

Back

If n is the first integer and m is the second integer, the sum can be represented as n + m. For example, if m is defined as n + k (where k is a constant), the inequality can be expressed as n + (n + k).

Front

What does the notation 'x < a or x > b' signify?

Back

This notation indicates that x can take any value that is either less than a or greater than b, meaning x is outside the interval [a, b].

Front

How do you solve a compound inequality of the form 'a < x + b < c'?

Back

To solve this compound inequality, you can break it into two separate inequalities: a < x + b and x + b < c. Then, isolate x in both inequalities to find the solution set.

Front

What is the significance of the 'and' in a compound inequality?

Back

The 'and' in a compound inequality indicates that both conditions must be satisfied simultaneously. For example, in 'a < x < b', x must be greater than a and less than b.

Front

What is the significance of the 'or' in a compound inequality?

Back

The 'or' in a compound inequality indicates that at least one of the conditions must be satisfied. For example, in 'x < a or x > b', x can be less than a or greater than b.

Front

How do you express the solution set for the inequality '-4 ≤ x ≤ 4'?

Back

The solution set for the inequality '-4 ≤ x ≤ 4' includes all real numbers x such that x is greater than or equal to -4 and less than or equal to 4.

Front

What is the first step in solving the inequality '45 < x + x + 7 < 52'?

Back

The first step is to simplify the inequality by combining like terms. In this case, you would combine the x terms: '45 < 2x + 7 < 52'.

Front

How do you find the integers that satisfy the inequality '44 < x + x + 5 < 88'?

Back

First, simplify the inequality to '44 < 2x + 5 < 88'. Then, isolate x by subtracting 5 from all parts and dividing by 2 to find the range of x.

Front

What is the general form of a compound inequality?

Back

The general form of a compound inequality can be expressed as 'a < x < b' or 'x < a or x > b', where a and b are constants.