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5 Feb 2026

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2 pages

Mastering Algebra: Simple Steps to Solve Equations

Scarlett Edwardes

@scarlett_1917

Algebraic equations might look intimidating with all those letters mixed... Show more

# SOLVING 'ALGEBRAIC' PROBLEMS

DESCRIPTION:
ALGEBRAIC EQUATIONS USE LETTERS TO REPRESENT NUMBERS, CREATING FORMULAE
THESE LETTERS CAN BE US

Solving Basic Algebraic Equations

Algebraic equations are basically mathematical puzzles where letters stand in for mystery numbers. Think of them as balance scales - whatever you do to one side, you must do to the other to keep things equal.

The golden rule is simple: isolate the variable (usually x) by doing the opposite operations. If something's being added, subtract it. If something's being multiplied, divide it.

Let's break down the process with $3x + 2 = 8 $. First, get rid of that +2 by subtracting 2 from both sides:$ 3x = 6 $. Then eliminate the 3 multiplying x by dividing both sides by 3:$ x = 2$.

Top Tip: Always work backwards through the order of operations - tackle addition and subtraction first, then multiplication and division!

For trickier examples like $0.5x - 3 = 20 $, the same rules apply. Add 3 to both sides to get$ 0.5x = 23 $, then multiply both sides by 2 (the opposite of dividing by 2) to find$ x = 46$.

Tackling Simultaneous Equations

Simultaneous equations are like solving two puzzles at once - you've got two unknowns (x and y) and two equations to work with. The trick is eliminating one variable to find the other.

Start by making one variable the same in both equations through multiplication. In our example, multiply the first equation by 3 and the second by 2 to get matching y coefficients: $24x + 6y = 138 $and$ 14x + 6y = 94$.

Now subtract one equation from the other to eliminate y completely. This gives us $10x = 44 $, so$ x = 4.4$. The hard part's done!

Remember: Once you've found one variable, substitute it back into either original equation to find the second one.

Pop $x = 4.4$ back into the first equation: $(8 \times 4.4) + 2y = 46$ . This gives us $35.2 + 2y = 46 $, so$ 2y = 10.8 $, and finally$ y = 5.4$. Job done!

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568

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5 Feb 2026

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2 pages

Mastering Algebra: Simple Steps to Solve Equations

Scarlett Edwardes

@scarlett_1917

Algebraic equations might look intimidating with all those letters mixed in with numbers, but they're actually just puzzles waiting to be solved! These equations use letters (like x and y) to represent unknown numbers, and once you learn the basic... Show more

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Solving Basic Algebraic Equations

The golden rule is simple: isolate the variable (usually x) by doing the opposite operations. If something's being added, subtract it. If something's being multiplied, divide it.

Let's break down the process with $3x + 2 = 8 $. First, get rid of that +2 by subtracting 2 from both sides:$ 3x = 6 $. Then eliminate the 3 multiplying x by dividing both sides by 3:$ x = 2$.

Top Tip: Always work backwards through the order of operations - tackle addition and subtraction first, then multiplication and division!

For trickier examples like $0.5x - 3 = 20 $, the same rules apply. Add 3 to both sides to get$ 0.5x = 23 $, then multiply both sides by 2 (the opposite of dividing by 2) to find$ x = 46$.

Sign up to see the contentIt's free!

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Join milions of students

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Tackling Simultaneous Equations

Simultaneous equations are like solving two puzzles at once - you've got two unknowns (x and y) and two equations to work with. The trick is eliminating one variable to find the other.

Now subtract one equation from the other to eliminate y completely. This gives us $10x = 44 $, so$ x = 4.4$. The hard part's done!

Remember: Once you've found one variable, substitute it back into either original equation to find the second one.

Pop $x = 4.4$ back into the first equation: $(8 \times 4.4) + 2y = 46$ . This gives us $35.2 + 2y = 46 $, so$ 2y = 10.8 $, and finally$ y = 5.4$. Job done!