# 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 $\scriptsize k{{a}^{x}}=m$ (where $\scriptsize x$ 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 $\scriptsize k{{a}^{{x+p}}}=m$ 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.