Examples for

# Common Core Math: High School Algebra: Reasoning with Equations & Inequalities

Equations and inequalities are two key types of mathematical statements: an equation uses the = symbol to connect two equal expressions, while an inequality describes a relationship between expressions using the symbols <, >, ≤ or ≥. In high school, students represent and analyze equations and inequalities in a variety of ways. In particular, students solve equations and inequalities algebraically by performing operations that isolate the desired variable. Students also analyze and solve equations and inequalities by graphing their solutions. Students solve sets of multiple equations or inequalities, called "systems," using algebraic and graphical methods and, at advanced levels, matrices.

### Common Core Standards

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### Solve Equations Graphically

Use plotting to visually determine solutions of equations and inequalities.

#### Graph equations in two variables on x and y axes (CCSS.Math.Content.HSA-REI.D.10):

#### Solve equations by graphing (CCSS.Math.Content.HSA-REI.D.11):

#### Solve systems of equations by graphing (CCSS.Math.Content.HSA-REI.C.6):

#### Graph the solution sets of systems of linear inequalities (CCSS.Math.Content.HSA-REI.D.12):

### Solve Equations Algebraically

Use algebraic operations to solve for an unknown variable in an equation or inequality.

#### Explain each step in solving an equation (CCSS.Math.Content.HSA-REI.A.1):

#### Solve rational and radical equations (CCSS.Math.Content.HSA-REI.A.2):

#### Solve linear equations and inequalities (CCSS.Math.Content.HSA-REI.B.3):

#### Solve quadratic equations (CCSS.Math.Content.HSA-REI.B.4):

### Solve Systems of Equations

Given multiple equations in multiple variables, solve for all unknowns.