Writing Equations and Inequalities from Word Problems

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables and constants.

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

How do you write an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express that relationship using mathematical symbols.

Front

What does 'y = mx + b' represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

In the equation 'y = 5x + 25', what does '5' represent?

Back

The number '5' represents the rate of change or slope, indicating that for each additional day, Alyssa reads 5 more pages.

Front

What does the term 'solution' mean in the context of equations?

Back

A solution is a value or set of values that makes an equation or inequality true.

Front

How do you solve the inequality '2p + 1 ≤ 10'?

Back

Subtract 1 from both sides to get '2p ≤ 9', then divide by 2 to find 'p ≤ 4.5'.

Front

What is the first step in solving the equation '300m + 1200 = 4500'?

Back

Subtract 1200 from both sides to isolate the term with the variable: '300m = 3300'.

Front

What does 'x + 6 ≥ 15' represent in a word problem?

Back

It represents that the total practice hours (x lessons of 2 hours each plus 6 hours already practiced) must be at least 15 hours.

Front

How do you express 'fewer than 30 miles' as an inequality?

Back

You can express it as 'x < 30', where 'x' is the total miles ridden.