4.5 Solving & Writing Equations and Inequalities

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 and shows that one is greater than, less than, or not equal to the other.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 7w + 5 = 3w - 15?

Back

The solution is w = -5.

Front

What is the solution to the equation 8w - 8 = -4x + 16?

Back

The solution is w = 2.

Front

How do you write an equation for a real-world problem?

Back

Identify the variables, constants, and relationships in the problem, then express them mathematically using an equation.

Front

What is the equation to determine the minimum number of cakes a bakery must sell to earn a profit?

Back

The equation is 15c > 1800 + 10c.

Front

What is the solution to the equation 7 + 6x - 7x = 3x - 2x - 5?

Back

The solution is x = 6.

Front

How do you compare two expressions to find when one is greater than the other?

Back

Set up an inequality that represents the relationship between the two expressions and solve for the variable.