Equations & Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the equation -11 - 5a = 6(5a + 4)?

Back

To solve, first distribute the 6: -11 - 5a = 30a + 24. Then, combine like terms and isolate 'a' to find a = -1.

Front

What is the solution set for the inequality -2x + 3(-4x + 6) ≤ 116?

Back

The solution set is x ≥ -7.

Front

How do you solve the equation 3x + 2(4x - 4) = 3?

Back

Distribute the 2: 3x + 8x - 8 = 3. Combine like terms and isolate 'x' to find x = 1.

Front

What is the solution to the equation 14p - 8 = 22 + 20p?

Back

To solve, rearrange the equation to isolate 'p': 14p - 20p = 22 + 8, resulting in p = -5.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms and distributing.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.