Inequality and Equations Flashcard

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include: x > 5, y ≤ 10.

Front

How do you solve the inequality 10 < 3x + 19?

Back

To solve, subtract 19 from both sides: 10 - 19 < 3x, which simplifies to -9 < 3x. Then divide by 3: -3 < x, or x > -3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or exactly equal to another value.

Front

How do you graph the inequality -2k > -6?

Back

To graph -2k > -6, first solve for k: k < 3. On a number line, draw an open circle at 3 and shade to the left.

Front

What is the solution to the inequality 3.6 - 4.85a ≥ -6.1?

Back

First, isolate a: 3.6 + 6.1 ≥ 4.85a, which simplifies to 9.7 ≥ 4.85a. Then divide by 4.85: a ≤ 2.

Front

What does the term 'solution set' refer to in inequalities?

Back

The solution set is the set of all values that satisfy the inequality. For example, the solution set for x > -3 is all numbers greater than -3.

Front

How do you interpret the inequality x < 3?

Back

The inequality x < 3 means that x can take any value less than 3, but not 3 itself.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to. For example, x > 2 does not include 2, but x ≥ 2 does.

Front

If Scott charges $35 for each car plus $7 per hour, how do you set up the equation for Kylie's car bill of $63?

Back

The equation is 35 + 7h = 63, where h is the number of hours worked.

Front

What is the first step to solve the equation 35 + 7h = 63?

Back

Subtract 35 from both sides: 7h = 28.