Forming Equations from Words

Forming & Solving Equations

Forming linear equations

How do I form expressions from words?

• You can turn common phrases into expressions

  • Use x to represent an unknown value

    2 less than "something"	$x-2$
    Double "something"	$2x$
    5 lots of "something"	$5x$
    3 more than "something"	$x+3$
    Half of "something"	$\frac{1}{2}x \mathrm{or} \frac{x}{2}$

• Common words indicating basic operations are:

  • Addition: sum, total, more than, increase

  • Subtraction: difference, less than, decrease

  • Multiplication: product, lots of, times as many, double, triple

  • Division: shared, split, grouped, halved, quartered

• Brackets help keep the order correct

  • "something" add 1, then multiplied by 3

    • $(x+1)\times 3$ which simplifies to $3(x+1)$

  • Compare this to "something" multiplied by 3, then add 1

    • $x\times 3+1$ which simplifies to $3x+1$

• You may have to choose which unknown to call x

  • If Adam is 10 years younger than Barry, then Barry is 10 years older than Adam

    • Either represent Adam's age as $x-10$ and Barry's age as $x$

    • Or represent Adam's age as $x$ and Barry's age as $x+10$

  • If Adam's age is half of Barry's age, then Barry's age is double Adam's age

    • So if Adam's age is $x$ then Barry's age is $2x$

    • This makes the algebra easier (rather than using $x$ for Barry's age and $\frac{1}{2}x$ for Adam's age)

How do I form equations?

• An equation is a statement with an equals sign that can be solved

• Try to put in the phrase "is equal to" to see where the equals goes

  • Lisa's age is double Aisha's age and the sum of their ages is ("is equal to") 27 

    • Represent Aisha's age as $x$ and Lisa's age is $2x$

    • The equation is $2x+x=27$

  • When solving, always give the answer in context

    • $3x=27$ so $x=9$

    • In context: "Lisa is 18 years old and Aisha is 9 years old"

• Sometimes you might have two unknown values (x  and y)

  • Use the information to form two simultaneous equations