MATHEMATICSAlgebra
Equations
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x
● Master Topic Guide Verified 11+ Curriculum
Solving Linear Equations Guide ⚖️
Master balancing equations, 4 golden rules, step-by-step worked examples, practice questions, and checking your solutions!
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SOLVING LINEAR EQUATIONS
An equation shows that two expressions are equal.
"Solving means finding the value of the unknown variable that makes the equation true!"
KEY VOCABULARY
| Equation | Math sentence with an equals sign (=). Ex: 2x + 3 = 11 |
| Variable | A letter (such as x) that stands for an unknown number. |
| Solution | The value of variable that makes equation true. In 2x + 3 = 11, x = 4 |
| Balance ⚖️ | Whatever you do to one side, you must do to the other side to keep it equal. |
THE RULES
Use these rules to keep the equation balanced while you solve:
➕ Add same number to both sidesx - 3 = 7 ➔ x = 7 + 3
➖ Subtract same number from both sidesx + 5 = 12 ➔ x = 12 - 5
✖️ Multiply both sides by same numberx/4 = 3 ➔ x = 3 × 4
➗ Divide both sides by same number6x = 30 ➔ x = 30 ÷ 6
⭐ The goal is to get the variable (x) by itself on one side!
Interactive Equation Balance Scale ⚖️
Step-by-step balance visualization
2x + 4 = 16
HOW TO SOLVE A LINEAR EQUATION (STEP BY STEP)
Example 1
Solve: x + 5 = 12
x + 5 ═ 12 Start here
x + 5 - 5 ═ 12 - 5 Subtract 5
x ═ 7 x by itself!
Check: 7 + 5 = 12 ✓
Example 2
Solve: 3x = 21
3x ═ 21 Start here
3x/3 ═ 21/3 Divide by 3
x ═ 7
Check: 3 × 7 = 21 ✓
Example 3
Solve: 2x + 4 = 16
2x + 4 ═ 16 Start here
2x + 4 - 4 ═ 16 - 4 Subtract 4
2x ═ 12 Divide by 2
x ═ 6
Check: 2(6) + 4 = 16 ✓
MORE EXAMPLES
1) Solve: x - 7 = 9
x - 7 + 7 ═ 9 + 7
x ═ 16
Check: 16 - 7 = 9 ✓
2) Solve: 4x = 32
4x/4 ═ 32/4
x ═ 8
Check: 4 × 8 = 32 ✓
3) Solve: x/5 = 6
x/5 × 5 ═ 6 × 5
x ═ 30
Check: 30/5 = 6 ✓
4) Solve: 5x - 10 = 25
5x ═ 35 ➔ x ═ 35/5
x ═ 7
Check: 5(7) - 10 = 25 ✓
TIPS TO REMEMBER
- ⚖️ Keep equation balanced. Do same to both sides.
- ( ) Undo addition/subtraction first, then multiply/divide.
- ❓ Move numbers without x across equals sign.
- ✔️ Always check answer in original equation.
COMMON MISTAKE
Forgetting to do the same thing on both sides!
x + 5 = 12
Wrong: x = 12 - 5 without showing balance ❌
Wrong: x = 12 - 5 without showing balance ❌
PRACTICE TIME!⭐ You've got this! Practice makes you better!
1) x + 6 = 15
x =
2) x - 9 = 14
x =
3) 2x = 18
x =
4) 3x + 7 = 22
x =
5) 5x = 45
x =
6) x/4 = 5
x =
7) 6x - 12 = 30
x =
8) 7x = 56
x =
9) 2x + 3 = 19
x =
10) x/3 = 9
x =
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