Writing Inequalities from Word Problems

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

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and translate the words into a mathematical expression.

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

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

'x' represents the number of hours Joan needs to babysit.

Subtract 10 from both sides to get 5x ≥ 90, then divide by 5 to find x ≥ 18.

To find the maximum hours, solve for x: 125x < 545, so x < 4.36 hours.

The phrase 'at least' indicates that the value can be equal to or greater than a certain number, represented by '≥'.

Subtract 7 from both sides to get 4x ≥ 12, then divide by 4 to find x ≥ 3.

It represents that the total height of the tree (currently 6 feet plus growth x) cannot exceed 35 feet.