GCSE Algebra Studio

GradeRealm • GCSE-aligned practice • Learn → Practice → Exam

⭐ 0 XP

🔥 0 solved

Practice: solve independently first. GradeRealm reveals hints and the visual model only when you need them.

Choose virtual class

📝

Visual worksheetQuestion 1 of 10

✓ First try 0

⚡ Avg efficiency 100%

↻ To retry 0

Skill: Two-step equations

Solve the equation and enter x.

One-step→Two-step→Negative values→x both sides→Brackets→Fractions→Form & solve

GRADEREALM • ALGEBRA VIRTUAL CLASS

Simultaneous Equations

Learn what a simultaneous solution means, then build through elimination, scaling, substitution and GCSE applications before taking a mixed checkpoint.

VISUAL WORKSHEET

Progressive simultaneous-equations practice

Original GradeRealm questions build from direct elimination through signed values, scaling, substitution, modelling and Higher-style mixed systems. Negative coefficients and negative solutions are deliberately included.

Questions

CONCEPT • LESSON 1 OF 6

What simultaneous equations mean

Answer-first graph checkAlgebra → coordinate → confirmation

Equation 1Equation 2Intersection / solutionYour checked point

TRY IT YOURSELF

Guided practice

Solve the pair. GradeRealm checks that your values satisfy both equations, not just one.

x =y =

Solve the equation

2x + 4 = 12

Two-step equations • Practice

Goal: get x on its own. Whatever you do to one side, do the same to the other side.

Exam mode: solve symbolically without hints or the visual model. Leave Exam mode when you are ready to review visually.

Symbolic2x + 4 = 12

What the model meansTwo x-tiles and four unit tiles balance twelve units.

Final answer

Type your answer whenever you think you know it. To complete the lab, you must also show the balancing steps.

x =

First, form an equation

Use x for the unknown in the context. An equivalent equation is accepted.

What just happened?

⚖️ Balanced

2x + 4

Left side

Right side

Make a move

Choose an operation and where to apply it. Both sides preserves equality. You can deliberately choose one side to see the balance break.

Mode

📝 Build a visual worksheet

Turn the lab into a marked worksheet. The GCSE mixed route now climbs deliberately from one-step equations to signed/negative solutions, x on both sides, brackets, fractional equations and forming equations from context.

Questions

Question mix

Board profile

Tier

Visual support

Worksheet results

Skill

GradeRealm controls the internal difficulty; learners see the mathematical skill instead of a level number.

100%Efficiency

0Moves

0Hints

Hint ladder

Hints become more specific each time. Using a hint slightly reduces the efficiency score.

Concept hint • −2%

Expand the brackets

The number outside the bracket multiplies every term inside it. Complete both products before the balance controls unlock.

x3 × x

+23 × 2

3(x + 2) → ?x + ?

Coefficient of x

Number term

Your expansion will appear here.

Clear the fraction

A fraction equation becomes easier when you multiply both sides by the denominator.

x + 4

What should you multiply both sides by?

Drag & drop algebra tiles

Drag a tile onto a pan. Drag an existing tile to the red remove zone. On touch devices, tap a tile then choose a target.

−x

−1

🗑 Drop an existing tile here to remove it from its pan

Write your own algebra step

GradeRealm recognises common written operations and equivalent one-step equations.

Symbolic ↔ visual explanation

Voice coach after each step

Operation

Value

Apply to

The green button previews the exact move before you apply it. For x-terms, 2 means 2x.

GCSE curriculum details

Curriculum metadata will appear here.

Question QA status will appear here.

Adaptive learning

Choose my next challenge from weak skills

Spaced review due0

Equation mastery map

Misconception profile

GradeRealm records patterns in your mistakes so practice can target the cause, not just the answer.

Diagnostic snapshot

GradeRealm will summarise strengths and recurring misconceptions as evidence builds.

Working

Start 2x + 4 = 12

Challenge complete

x = 4

You preserved equality, isolated x and entered the final answer.