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Forming Linear Equations
Select the skills to practice, and then click Go!
Foundational Skills
Translate addition phrases
\[ x + 5 \]
Translate simple addition phrases into expressions.
Translate subtraction phrases
\[ x – 6 \]
Translate subtraction phrases paying attention to order.
Translate multiplication phrases
\[ 3x \]
Translate multiplication phrases into expressions.
Translate division phrases
\[ \frac{x}{4} \]
Translate division phrases into expressions.
Translate two-operation phrases
\[ 2x + 5 \]
Translate phrases involving two operations.
Recognise when brackets are needed
\[ 2(x + 3) \]
Recognise when a sum/difference is then operated on.
I Think of a Number (One-Step)
Form one-step addition equation
\[ x + 7 = 15 \]
Form an equation involving addition.
Form one-step subtraction equation
\[ x – 4 = 9 \]
Form an equation involving subtraction.
Form one-step multiplication equation
\[ 5x = 30 \]
Form an equation involving multiplication.
Form one-step division equation
\[ \frac{x}{3} = 8 \]
Form an equation involving division.
I Think of a Number (Two-Step)
Form equation (multiply then add/subtract)
\[ 2x + 5 = 17 \]
Multiply then add or subtract structure.
Form equation (divide then add/subtract)
\[ \frac{x}{4} + 3 = 10 \]
Divide then add OR subtract structure.
Form equation (add/subtract then multiply)
\[ 2(x + 3) = 16 \]
Requires brackets – add/subtract before multiply.
Form equation from ‘more than’ phrasing
\[ 2x + 7 = 23 \]
“7 more than twice a number is 23”
Form equation from ‘less than’ phrasing
\[ 3x – 4 = 17 \]
“4 less than triple a number is 17”
I Think of a Number (x on Both Sides)
Form equation with x on both sides
\[ 4x + 3 = 2x + 11 \]
Same unknown appears on both sides.
Form equation with different operations
\[ 3x + 5 = 2(x + 11) \]
Both sides from different operation sequences.
I Think of a Number (Brackets)
Form equation with single bracket
\[ 2(x + 4) = 22 \]
Form an equation requiring a single bracket.
Form equation with bracket then operation
\[ 4(x – 3) + 5 = 33 \]
Bracket followed by additional operation.
Form equation with brackets on both sides
\[ 3(x + 2) = 2(x + 5) \]
Brackets appear on both sides.
Form three-step equation
\[ \frac{2x + 5}{3} = 7 \]
Three operations in sequence.
Form complex bracketed equation
\[ 2(x – 1) + 3x = 33 \]
Brackets with additional x terms.
Perimeter Problems
Form equation from rectangle perimeter
\[ 2(x + 3) + 2(4) = 30 \]
Rectangle perimeter problem.
Form equation from triangle perimeter
\[ x + (x + 2) + 7 = 21 \]
Triangle perimeter problem.
Form equation from square perimeter
\[ 4(2x – 1) = 28 \]
Square perimeter problem.
Form equation from equal perimeters
\[ 2(x + 5) + 6 = 4x \]
Two shapes with equal perimeters.
Area Problems
Form equation from rectangle area
\[ 5(x + 2) = 40 \]
Rectangle area problem.
Form equation from triangle area
\[ \frac{2x \times 6}{2} = 24 \]
Triangle area problem.
Form equation from equal areas
\[ 3(x + 4) = 6(x – 1) \]
Two shapes with equal areas.
Cost and Quantity Problems
Form equation from total cost
\[ 5x + 3.50 = 10 \]
Cost and change problem.
Form equation from two item types
\[ 30x + 80 = 190 \]
Two different items problem.
Form equation from equal spending
\[ 3x + 5 = 5x \]
Two people spend equal amounts.
Age Problems
Form equation from age sum
\[ x + (x + 4) = 22 \]
Ages summing to a total.
Form equation from age multiple
\[ x + 3x = 52 \]
Age as a multiple relationship.
Form equation from future ages
\[ x + 5 = 2x \]
Future age relationships.
Form equation from past ages
\[ x – 5 = \frac{x}{2} \]
Past age relationships.
Consecutive Number Problems
Form equation from consecutive integers
\[ n + (n+1) + (n+2) = 54 \]
Consecutive integers summing to a total.
Special Cases
Form equation (solution would be zero)
\[ 3x + 5 = 5 \]
Equation where solving gives x = 0.
Form equation (solution would be negative)
\[ 2x + 15 = 7 \]
Equation where solving gives negative x.
Recognise when equation cannot be formed
\[ \text{Cannot form} \]
Insufficient information to form equation.
Timer (Optional)
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