Solving Inequalities Concept Check

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is less than 3.

Front

How do you solve the inequality 9.55 < 3.5x + 19?

Back

To solve, subtract 19 from both sides: 9.55 - 19 < 3.5x, then divide by 3.5 to find x > -2.7.

Front

What is the solution to the inequality 2(b - 8) > 12?

Back

The solution is b > 14.

Front

How do you graph the inequality -4(x + 3) ≤ -56?

Back

First, solve for x: x + 3 ≥ 14, then x ≥ 11. Shade the region to the right of x = 11.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.

Front

Back

First, convert mixed numbers to improper fractions, then isolate x to find x > -10.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality.