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Linear Equations with Brackets
Select the skills to practice, and then click Go!
Foundational skills
Expand a single bracket
\[ 3(x + 4) = 3x + 12 \]
Expand a bracket by multiplying each term inside by the number outside.
Expand a bracket with subtraction inside
\[ 4(x – 2) = 4x – 8 \]
Expand a bracket containing subtraction.
Expand with negative multiplier
\[ -2(x + 5) = -2x – 10 \]
Expand a bracket where the multiplier is negative.
Single bracket equations
Solve a(x + b) = c
\[ 3(x + 2) = 21 \]
Solve equations with a single bracket containing addition.
Solve a(x – b) = c
\[ 4(x – 3) = 20 \]
Solve equations with a single bracket containing subtraction.
Solve a(bx + c) = d
\[ 2(3x + 4) = 26 \]
Solve equations where the bracket contains a coefficient on x.
Solve a(bx – c) = d
\[ 3(2x – 1) = 27 \]
Solve equations where the bracket contains a coefficient on x and subtraction.
Single bracket – negative answer
\[ 2(x + 5) = 4 \]
Solve single bracket equations where the answer is a negative integer.
Single bracket – fractional answer
\[ 3(x + 1) = 8 \]
Solve single bracket equations where the answer is a fraction.
Bracket plus constant
Solve a(x + b) + c = d
\[ 2(x + 3) + 5 = 17 \]
Solve equations with a bracket and an additional constant term.
Solve a(x – b) + c = d
\[ 3(x – 2) + 4 = 19 \]
Solve equations with a bracket containing subtraction plus an additional constant.
Solve a(x + b) – c = d
\[ 4(x + 1) – 3 = 17 \]
Solve equations with a bracket and a subtracted constant term.
Bracket + constant – negative answer
\[ 2(x + 4) + 3 = 7 \]
Solve bracket plus constant equations where the answer is a negative integer.
Bracket + constant – fractional answer
\[ 3(x + 2) + 1 = 12 \]
Solve bracket plus constant equations where the answer is a fraction.
Bracket with x term outside
Solve a(x + b) + cx = d
\[ 2(x + 3) + 4x = 24 \]
Solve equations with a bracket and an additional x term outside.
Solve a(x + b) – cx = d
\[ 5(x + 2) – 2x = 22 \]
Solve equations with a bracket minus an x term.
Bracket + x term – negative answer
\[ 3(x + 5) + 2x = 10 \]
Solve equations with bracket and x term outside where the answer is negative.
Multiple brackets on one side
Solve a(x + b) + c(x + d) = e
\[ 2(x + 3) + 3(x + 1) = 24 \]
Solve equations with two brackets on one side (both addition inside).
Solve a(x + b) + c(x – d) = e
\[ 3(x + 2) + 2(x – 1) = 24 \]
Solve equations with two brackets – one addition and one subtraction inside.
Solve a(x + b) – c(x + d) = e
\[ 4(x + 2) – 2(x + 1) = 12 \]
Solve equations where the second bracket is subtracted.
Multiple brackets – negative answer
\[ 2(x + 4) + 3(x + 2) = 9 \]
Solve equations with multiple brackets where the answer is a negative integer.
Multiple brackets – fractional answer
\[ 2(x + 1) + 3(x + 2) = 15 \]
Solve equations with multiple brackets where the answer is a fraction.
Brackets with x on both sides
Solve a(x + b) = cx + d
\[ 3(x + 2) = x + 14 \]
Solve equations where a bracket on one side leads to x terms on both sides.
Solve a(x – b) = cx + d
\[ 4(x – 1) = 2x + 6 \]
Solve equations where a bracket with subtraction leads to x on both sides.
Solve a(x + b) = d – cx
\[ 2(x + 5) = 18 – x \]
Solve equations where expanding leads to a – cx term on the right.
Solve ax + b = c(x + d)
\[ 5x + 4 = 2(x + 8) \]
Solve equations where the bracket is on the right side.
x both sides – negative answer
\[ 3(x + 4) = x + 6 \]
Solve bracket equations with x on both sides where the answer is negative.
x both sides – fractional answer
\[ 4(x + 2) = x + 11 \]
Solve bracket equations with x on both sides where the answer is a fraction.
Brackets on both sides
Solve a(x + b) = c(x + d)
\[ 4(x + 1) = 2(x + 5) \]
Solve equations with brackets on both sides.
Solve a(x – b) = c(x + d)
\[ 5(x – 1) = 2(x + 5) \]
Solve equations with brackets on both sides – subtraction and addition.
Solve a(x – b) = c(x – d)
\[ 4(x – 3) = 2(x – 1) \]
Solve equations with subtraction inside brackets on both sides.
Brackets both sides – negative answer
\[ 3(x + 5) = 2(x + 2) \]
Solve equations with brackets on both sides where the answer is negative.
Brackets both sides – fractional answer
\[ 5(x + 1) = 3(x + 2) \]
Solve equations with brackets on both sides where the answer is a fraction.
Negative multipliers
Solve -a(x + b) = c
\[ -2(x + 4) = -14 \]
Solve equations where the bracket has a negative multiplier.
Solve -a(x – b) = c
\[ -3(x – 2) = -12 \]
Solve equations where a negative multiplier meets subtraction inside the bracket.
Solve a(x + b) = -c(x – d)
\[ 2(x + 5) = -3(x – 8) \]
Solve equations where one bracket has a negative multiplier and there are brackets on both sides.
Negative multiplier – negative answer
\[ -2(x + 1) = 6 \]
Solve negative multiplier equations where the answer is negative.
Special cases
Bracket where x terms simplify
\[ 3(x + 2) – 2x = 11 \]
Solve equations where the bracket expands but x terms simplify.
Equation with solution x = 0
\[ 3(x + 4) = 12 \]
Solve bracket equations where the solution is zero.
Equation with solution x = 1
\[ 2(x + 3) = 8 \]
Solve bracket equations where the solution is one.
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