Solving 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, greater than or equal to, or less than or equal to the other.

Front

How do you solve a simple equation like 4 + m = 10?

Back

To solve for m, subtract 4 from both sides: m = 10 - 4, so m = 6.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves drawing a number line or coordinate plane to represent the set of solutions that satisfy the inequality.

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.

Front

How do you write an inequality for a situation?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using inequality symbols.

Front

What is the solution to the inequality 30 + 20x < 15 + 30x?

Back

To solve, subtract 20x from both sides: 30 < 15 + 10x, then subtract 15: 15 < 10x, and divide by 10: x > 1.5.

Front

If a chef has 7 pounds of potatoes and needs more than 14 pounds, how do you express this as an inequality?

Back

The inequality is x + 7 > 14, where x is the amount of potatoes the chef needs to buy.

Front

What is the first step in solving the equation 19 + a = -50?

Back

Subtract 19 from both sides: a = -50 - 19, so a = -69.

Front

How do you determine the maximum time Shari can spend on science homework if she has 40 minutes total?

Back

Set up the inequality: s ≤ 40 - 23, which simplifies to s ≤ 17.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to another value.