# Functions and algebra: Solve algebraic equations and inequalities

### Subject outcome 2.3

Solve algebraic equations and inequalities

### Learning outcomes

- Solve linear equations.
- Solve quadratic equations by factorisation.
- Solve exponential equations of the form [latex]\scriptsize k{{a}^{x}}=m[/latex] (where [latex]\scriptsize x[/latex] is an integer) by using the laws of exponents.
- Solve inequalities in one variable and represent the solution in set builder notation, interval notation and on a number line.
- Solve simultaneous equations with two unknowns algebraically and graphically, where both equations are linear.

### Unit outcomes: Unit 1: Solve linear and quadratic equations

By the end of this unit you will be able to:

- Solve equations with a single variable which are called linear equations
- Solve equations with a single variable that is squared (quadratic equations) by factorisation.

### Unit outcomes: Unit 2: Solve exponential and literal equations

By the end of this unit you will be able to:

- Solve exponential equations of the form [latex]\scriptsize k{{a}^{{x+p}}}=m[/latex] by using the laws of exponents.
- Solve literal equations.

### Unit outcomes: Unit 3: Solve algebraic inequalities

By the end of this unit you will be able to:

- Solve linear inequalities with a single unknown or variable.
- Represent the solution to linear inequalities:
- In set builder notation
- In interval notation
- On the number line.

### Unit outcomes: Unit 4: Solve simultaneous equations

By the end of this unit you will be able to:

- Solve systems of simultaneous equations where both equations are linear equations algebraically by means of:
- Elimination
- Substitution.

- Solve systems of simultaneous equations where both equations are linear equations graphically by finding the point of intersection of the functions.