Common Core · High school
HSA-REI.B.3
High school — Solve linear equations and inequalities in one variable, including with letters for coefficients.
High school — Solve linear inequalities in one variable, including with letters for coefficients.
High school — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
High school — Solve linear equations and inequalities in one variable, including compound inequalities.
The 4 skills that cover it
- Multi-Step EquationsSolve equations that need distributing, combining like terms, or moving variables to one side.Read the lesson →
- Linear InequalitiesSolve inequalities the way you solve equations, with one extra rule: multiplying or dividing by a negative flips the sign.Read the lesson →
- Literal Equations & FormulasRearrange a formula to isolate any one of its letters, using the same moves as a numeric equation, and use the rearranged form to solve for the quantity you actually need.Read the lesson →
- Absolute Value & Compound InequalitiesSolve equations with an absolute value by splitting them into two cases, and solve compound inequalities joined by "and" or "or", writing each solution as an interval on the number line.Read the lesson →
What a student should be able to do
- Distribute and combine like terms before solving.
- Solve equations with the variable on both sides.
- Recognise equations with no solution or infinitely many solutions.
- Translate multi-step word problems into equations.
- Solve one- and two-step inequalities.
- Flip the inequality sign when multiplying or dividing by a negative.
- Graph a solution set on a number line.
- Write and solve inequalities from constraint word problems.
- Solve a formula such as p = 2l + 2w for one of its variables.
- Isolate a variable that appears inside a fraction or multiplied by another letter.
- Choose the rearrangement that matches a given formula.
- Rearrange a formula and then evaluate it for given values.
- Solve |x - a| = b and |ax + b| = c, giving both solutions.
- Solve an "and" compound inequality such as -3 < 2x + 1 <= 7.
- Solve an "or" compound inequality and describe its solution set.
- Solve an absolute value inequality and write the solution as a compound inequality.