In mathematics, a solution is the value or values that satisfy an equation or inequality. When we solve an equation or inequality, we are looking for the solution or solutions that make the statement true.

There are different types of solutions based on the type of equation or inequality being solved:

**One Solution:**An equation has one solution when there is only one value that makes the equation true.**No Solution:**An equation has no solution when there is no value that makes the equation true.**Infinitely Many Solutions:**An equation has infinitely many solutions when any value of the variable makes the equation true. This often occurs in the case of identities or equations where the variable can be eliminated.

There are various methods to find solutions to equations and inequalities:

**Algebraic Methods:**This involves using algebraic techniques such as simplifying, factoring, and isolating the variable to find the solution.**Graphical Methods:**Graphing the equation or inequality on a coordinate plane and identifying the points of intersection with the x-axis to find solutions.**Numeric Methods:**Using numerical methods such as trial and error, or using a calculator to approximate solutions.

When studying solutions in mathematics, it's important to:

- Understand the different types of solutions and how to recognize them.
- Practice solving equations and inequalities using algebraic, graphical, and numeric methods.
- Master the techniques for finding solutions, such as isolating the variable or graphing the equation.
- Review the properties of equations and inequalities to determine the number of solutions.

Study GuideDiameter of Circle Worksheet/Answer key

Diameter of Circle Worksheet/Answer key

Diameter of Circle Worksheet/Answer key

Diameter of Circle

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.