$6x+15$. Multiply each term inside the bracket by 3: $3\\times 2x=6x$ and $3\\times 5=15$.

$x=5$. Subtract 7 from both sides: $x=12-7=5$.

$x=7$. Divide both sides by 3: $x=21\\div 3=7$.

$3(2x+3)$. The highest common factor of 6 and 9 is 3, giving $3(2x+3)$.

AQA · GCSE Maths 8300

AQA GCSE Maths: Algebra — Practice Questions & Answers

Q: Simplify $5a+3b-2a+4b$.

$3a+7b$. Collect like terms: $5a-2a=3a$ and $3b+4b=7b$.

Q: Simplify $x^{3}\\times x^{4}$.

$x^{7}$. When multiplying powers of the same base, add the indices: $3+4=7$.

Q: What is the next term in the arithmetic sequence $4, 7, 10, 13, \\ldots$?

$16$. The common difference is $+3$, so the next term is $13+3=16$.

Q: In the line $y=3x+2$, what is the gradient?

$3$. In $y=mx+c$ the gradient is $m$, which is 3 here.

Q: Solve the inequality $x+4\\gt 9$.

$x\\gt 5$. Subtract 4 from both sides to get $x\\gt 5$.

Q: Expand and simplify $(x+3)(x+5)$.

$x^{2}+8x+15$. Use FOIL: $x^{2}+5x+3x+15=x^{2}+8x+15$.

A complete walk through GCSE Algebra: manipulating expressions, expanding and factorising, solving and rearranging, straight-line and curved graphs, simultaneous equations, inequalities, sequences, functions and iteration. Each section builds the techniques and shows the standard exam methods.

834 practice questions available for this topic — here are 10 with full answers and explanations.

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Practice questions with answers

1 Multiple choice · Easy

Simplify $5a+3b-2a+4b$.

$3a+7b$
$7a+7b$
$3a+b$
$10ab$

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2 Multiple choice · Easy

Simplify $x^{3}\\times x^{4}$.

$x^{7}$
$x^{12}$
$x^{1}$
$2x^{7}$

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3 Multiple choice · Easy

Expand $3(2x+5)$.

$6x+15$
$6x+5$
$5x+8$
$2x+15$

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4 Multiple choice · Easy

Solve $x+7=12$.

$x=5$
$x=19$
$x=-5$
$x=84$

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5 Multiple choice · Easy

Solve $3x=21$.

$x=7$
$x=18$
$x=63$
$x=24$

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6 Multiple choice · Easy

Factorise $6x+9$.

$3(2x+3)$
$3(2x+9)$
$6(x+3)$
$3(6x+9)$

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7 Multiple choice · Easy

What is the next term in the arithmetic sequence $4, 7, 10, 13, \\ldots$?

$16$
$15$
$17$
$26$

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8 Multiple choice · Easy

In the line $y=3x+2$, what is the gradient?

$3$
$2$
$5$
$\\frac{1}{3}$

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9 Multiple choice · Easy

Solve the inequality $x+4\\gt 9$.

$x\\gt 5$
$x\\lt 5$
$x\\gt 13$
$x\\gt 36$

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10 Multiple choice · Medium

Expand and simplify $(x+3)(x+5)$.

$x^{2}+8x+15$
$x^{2}+15x+8$
$x^{2}+15$
$x^{2}+2x+15$

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Key terms in Algebra

Algebra: The branch of mathematics that uses letters and symbols to represent numbers and quantities in expressions and equations.

Variable: A letter that represents an unknown or changing value, such as $x$ or $y$.

Constant: A fixed number whose value does not change, such as the $5$ in $3x + 5$.

Term: A single number, variable, or product of them in an expression, such as $4x$ or $7$ in $4x + 7$.

Coefficient: The number multiplying a variable in a term. In $6y$ the coefficient is $6$.

Expression: A combination of numbers, variables and operations with no equals sign, such as $3x + 2$.

Equation: A mathematical statement that two expressions are equal, containing an equals sign, such as $2x + 1 = 7$.

Identity: An equation that is true for all values of the variable, often shown with the symbol $\\equiv$.

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AQA GCSE Maths: Algebra — Practice Questions & Answers

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Key terms in Algebra

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