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Substitution

T1_LO8 · lo-yr9-substitution

Complete
Key idea:

Substitution means replacing a variable with its value, then simplifying carefully. If $x=3$, then every $x$ is replaced by $3$.

Steps

  1. Write the value of the variable clearly.

  1. Replace each variable with that value.

  1. Use brackets if needed, especially with negatives.

  1. Work out the expression using GEMA.

Key facts

  • If $x=4$, then $2x=8$.

  • If $a=5$, then $a^2=25$.

  • If $p=3$ and $q=2$, then $p+2q=7$.

  • Brackets matter: if $x=-2$, then $x^2=4$ but $-x^2=-4$.

Common mistake

Forgetting brackets with negatives. If $x=-3$, then $x^2=(-3)^2=9$, not $-9$.

Try these
  1. If $x=3$, find $x+4$.

  2. If $a=5$, find $2a$.

  3. If $m=2,n=4$, find $m+n$.

Example 1: one variable

If $x=4$, find $2x+3$.$$ 2x+3=2(4)+3=8+3=11 $$

Example 2: two variables

If $p=5$ and $q=2$, find $p+2q$.$$ p+2q=5+2(2)=5+4=9 $$

Example 3: powers

If $a=3$, find $a^2+1$.$$ a^2+1=3^2+1=9+1=10 $$

Example 4: negative value

If $x=-2$, find $x^2+3$.$$ x^2+3=(-2)^2+3=4+3=7 $$