Solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be either less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

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

Front

How do you solve the inequality x + 4 ≤ -18?

Back

Subtract 4 from both sides: x ≤ -18 - 4, which simplifies to x ≤ -22.

Front

What is the solution set for the inequality x > -4?

Back

The solution set is {x | x > -4}, meaning all numbers greater than -4.

Front

How do you graph the inequality x < -2?

Back

Draw a number line, place an open circle at -2, and shade to the left to indicate all numbers less than -2.

Front

What is the first step to solve -2(x + 2) < 14?

Back

Distribute -2: -2x - 4 < 14.

Front

What is the solution to the inequality 2x - 3 ≥ 4x - 1?

Back

Rearranging gives -2x ≥ 2, which simplifies to x ≤ -1.

Front

What does it mean to 'translate' a word problem into an inequality?

Back

It means to convert a verbal statement into a mathematical expression using inequality symbols.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

After solving, the solution is x > -9.