MathsFreePrintable

Exploring Equations

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Exploring Equations

Solve each equation or complete the task given, and show your working where space is provided. Check solutions by substituting them back into the original equation where applicable.

Decode the equations

Identify equation types and spot what makes a solution work.

1.A puzzle uses the equation 4x − 7 = 13. Which value of x makes the equation true?

x = 4
x = 5
x = 6
x = 20

2.Classify each equation as linear or quadratic: (a) 3x + 8 = 20; (b) x² − 7x + 12 = 0. Give one clue you used.

3.Mere solves 2(x + 3) = 18 and gets x = 6. Is Mere correct? Substitute x = 6 into the original equation to justify your answer.

TrueFalse

Solve and check

Use inverse operations to find each unknown. Keep both sides balanced.

4.A food truck sells wraps for $7 each and charges a one-off $3 delivery fee. The total is $38. Write and solve an equation to find how many wraps were ordered.

5.Solve 5 − 2x = 17. Show the inverse operations you use.

6.Solve 3(x − 2) = 2x + 5, then check your answer in the original equation.

7.Solve the quadratic equation x² − 9 = 0. Give both solutions.

8.Factorise x² − 5x + 6 and use your factors to solve x² − 5x + 6 = 0.

9.The number line shows the two roots of a quadratic equation. Write the roots from least to greatest, then write a monic quadratic equation that has these roots.