Solving equations and inequalities

Front

What is an inequality?

Back

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

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does the solution x ≥ -10 represent?

Back

It means that x can be any number greater than or equal to -10.

Front

What is the solution to the equation 15 - ½x = 21 when x = -12?

Back

Substituting -12 gives: 15 - ½(-12) = 15 + 6 = 21, which is true.

Front

What does 'no solution' mean in the context of inequalities?

Back

It means that there are no values of the variable that satisfy the inequality.

Front

How do you solve the inequality 3x - 8 < 3(x - 4) + 1?

Back

1. Expand the right side: 3x - 8 < 3x - 12 + 1. 2. Simplify: 3x - 8 < 3x - 11. 3. This leads to -8 < -11, which is false.

Front

What is the solution to the inequality -3 - 6(4x + 6) > -111?

Back

1. Distribute: -3 - 24x - 36 > -111. 2. Combine like terms: -24x > -72. 3. Divide by -24 (flip the inequality): x < 3.

Front

What does the inequality x ≤ 20 represent in a real-world context?

Back

It means you can spend 20 dollars or less on a birthday present.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater or less than another.

Front

How do you graph the solution x ≥ -10 on a number line?

Back

Draw a solid dot at -10 and shade to the right to indicate all numbers greater than or equal to -10.