AQA · Mathematics · 8300
GCSE Maths: Equations: letters both sides
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Equations: letters both sides (Corbettmaths Video 113), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the first step when solving an equation with letters on both sides?
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Collect all the terms containing the variable on one side of the equation (usually by adding or subtracting).
Solve: 7w + 3 = 5w + 9
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w = 3. (Subtract 5w from both sides: 2w + 3 = 9, then subtract 3: 2w = 6, divide by 2.)
Why does the equation 8x + 3 = 2(4x + 1) have no solution?
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When expanded, 2(4x + 1) = 8x + 2, so the equation becomes 8x + 3 = 8x + 2. Subtracting 8x from both sides gives 3 = 2, which is false. No value of x can satisfy this.
Solve: 9x − 2 = 3x + 70
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x = 12. (Subtract 3x from both sides: 6x − 2 = 70, add 2: 6x = 72, divide by 6.)
Solve: 8x + 1 = 6 − 2x
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x = 0.5. (Add 2x to both sides: 10x + 1 = 6, subtract 1: 10x = 5, divide by 10.)
Solve: 7x = 61.6 − 4x
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x = 5.6. (Add 4x to both sides: 11x = 61.6, divide by 11.)
Solve: 7y + 6 = 5(y − 2)
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y = −8. (Expand: 7y + 6 = 5y − 10, subtract 5y: 2y + 6 = −10, subtract 6: 2y = −16, divide by 2.)
Solve: 4(2x − 5) = 5x + 4
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x = 8. (Expand: 8x − 20 = 5x + 4, subtract 5x: 3x − 20 = 4, add 20: 3x = 24, divide by 3.)
Solve: 2(2x + 1) = 3(x − 4)
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x = −14. (Expand: 4x + 2 = 3x − 12, subtract 3x: x + 2 = −12, subtract 2: x = −14.)
What is the first step to solve 3x = -24?
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Divide both sides by 3 to isolate x.
When solving 2w - 1 = 13, what should you do first?
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Add 1 to both sides to isolate the term with the variable.
In the equation 9c - 4 = 68, what is the value of c?
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c = 8. (Add 4 to get 9c = 72, then divide by 9.)
How do you simplify 5y + y before solving 5y + y = 60?
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Combine like terms to get 6y.
When solving x/2 + 3 = 10, what do you do after subtracting 3 from both sides?
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Multiply both sides by 2 to isolate x.
In the equation 12 - y = 5, what is the value of y?
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y = 7. (Rearrange to get y = 12 - 5.)
When solving 3x/4 = 9, what operation isolates x?
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Multiply both sides by 4, then divide by 3 (or multiply by 4/3).
What is the first step to solve 3(y + 4) = 24?
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Expand the brackets by distributing: 3y + 12 = 24.
When solving 3(4w - 1) = 39, what do you get after expanding the brackets?
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12w - 3 = 39.
When solving 12x + 3 = 7x - 4, what simplified equation do you get after collecting variable terms?
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5x + 3 = -4 (after subtracting 7x from both sides).
What is the solution to 5(3c - 2) - 7c = 40 - 2c?
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c = 5
In the grid system where each row sums to a given total, if w + w + w + w = 20, what is the value of w?
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w = 5
In the grid problem, if w = 5 and w + w + x + x = 24, what is the value of x?
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x = 7
In the grid problem, if w = 5, x = 7, and w + x + x + y = 25, what is the value of y?
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y = 6
In the grid problem, if w = 5, x = 7, y = 6, and w + x + y + z = 30, what is the value of z?
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z = 12
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