Equations and Inequalities Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include <, >, ≤, and ≥.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or exactly equal to another value.

Front

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

Back

1. Distribute: 3x + 8x - 8 = 3. 2. Combine like terms: 11x - 8 = 3. 3. Add 8 to both sides: 11x = 11. 4. Divide by 11: x = 1.

Front

What is the equation for the total cost c of hitting b buckets of golf balls if it costs $4 to rent a golf club and $2.75 per bucket?

Back

c = 2.75b + 4.

Front

What does the slope of a line represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you graph the inequality x < -4?

Back

Draw a number line, place an open circle at -4 (indicating -4 is not included), and shade to the left to show all numbers less than -4.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

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 than or less than another.