T1_LO8 · lo-yr9-substitution
Substitution means replacing a variable with its value, then simplifying carefully. If $x=3$, then every $x$ is replaced by $3$.
Steps
Write the value of the variable clearly.
Replace each variable with that value.
Use brackets if needed, especially with negatives.
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 $-x^2=-4$.
Forgetting brackets with negatives. If $x=-3$, then $x^2=(-3)^2=9$, not $-9$.
If $x=3$, find $x+4$.
If $a=5$, find $2a$.
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 $x^2+3$.$$ x^2+3=(-2)^2+3=4+3=7 $$