Getting Started with Single Variable Equations

Think of algebraic equations as detective work - you're hunting for the mystery number hiding behind a letter. When you see something like x + 3 = 10, you're really being asked "what number plus 3 equals 10?"

The golden rule is simple: do the opposite of what's been done to your unknown letter. If something's been added, subtract it. If something's been subtracted, add it back.

Let's crack x + 3 = 10. Since 3 was added to x, we subtract 3 from the other side: 10 - 3 = 7. So x = 7! Don't worry if the equation looks backwards like 14 = a - 5 - just flip it around to a - 5 = 14, then add 5 to both sides to get a = 19.

Quick Tip: Always check your answer by plugging it back into the original equation!

Tackling Multiplication and Division

Now we're dealing with multiplication and division, but honestly, it's just as straightforward. The same "do the opposite" rule applies - if your unknown is being multiplied, you divide, and vice versa.

Take b × 3 = 18. Since b is multiplied by 3, we divide both sides by 3: 18 ÷ 3 = 6. Therefore b = 6! Easy peasy.

When you see something like 8 = f ÷ 2, flip it if it helps: f ÷ 2 = 8. Since f is being divided by 2, multiply both sides by 2: 8 × 2 = 16, so f = 16.

Remember: Multiplication and division are opposites, just like addition and subtraction!

The beauty of algebra is that once you've mastered this "opposite operation" technique, you can solve loads of different equations using the exact same method.