Inequalities Flashcard Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

How do you solve the inequality: 7 + 2 ≥ -2m + 2 - 3?

Back

First, simplify the right side: 7 + 2 ≥ -2m - 1. Then, isolate m: 9 + 1 ≥ -2m, which simplifies to 10 ≥ -2m, leading to m ≥ -5.

Front

What does the solution m ≥ -5 represent on a number line?

Back

It represents all numbers greater than or equal to -5, including -5 itself.

Front

What is the first step in solving the inequality -138 ≥ -6(6b - 7)?

Back

Distribute -6 to both terms inside the parentheses: -138 ≥ -36b + 42.

Front

How do you isolate b in the inequality -138 ≥ -36b + 42?

Back

Subtract 42 from both sides: -180 ≥ -36b, then divide by -36 (remember to flip the inequality): b ≥ 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

Back

Multiply both sides by 2: -w + 6 < 10. Then, isolate w: -w < 4, leading to w > -4.

Front

What is the meaning of the inequality 2(x + 2) < 3x - 8?

Back

It represents a condition where twice the sum of a number x and 2 is less than three times the number x minus 8.

Front

How do you graph the solution to an inequality?

Back

To graph the solution, plot the number line and use an open circle for '<' or '>' and a closed circle for '≤' or '≥'. Shade the region that satisfies the inequality.