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 GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.