Simple Substitution

Evaluate $2x + 7$ when $x = 5$

Write the original expression: $2x + 7$ = Ready to substitute

Replace $x$ with $5$: $2(5) + 7$ = Substitution complete

Multiply first (order of operations): $10 + 7$ = Multiplication done

Add to get the final answer: $10 + 7 = 17$ = $17$

Answer: When $x = 5$, the expression $2x + 7$ equals $17$

Two Variables

Evaluate $3a - 2b$ when $a = 4$ and $b = 3$

Write the original expression: $3a - 2b$ = Ready to substitute

Replace $a$ with $4$ and $b$ with $3$: $3(4) - 2(3)$ = Both variables substituted

Multiply each term: $12 - 6$ = Multiplications complete

Subtract to get the final answer: $12 - 6 = 6$ = $6$

Answer: When $a = 4$ and $b = 3$, the expression $3a - 2b$ equals $6$

Expression with Exponents

Evaluate $x^2 + 3x - 4$ when $x = 3$

Write the original expression: $x^2 + 3x - 4$ = Ready to substitute

Replace $x$ with $3$: $(3)^2 + 3(3) - 4$ = Substitution complete

Calculate the exponent first: $9 + 3(3) - 4$ = $3^2 = 9$

Then multiply: $9 + 9 - 4$ = $3 \times 3 = 9$

Add and subtract left to right: $9 + 9 - 4 = 14$ = $14$

Answer: When $x = 3$, the expression $x^2 + 3x - 4$ equals $14$

Expression with Parentheses

Evaluate $2(n + 5) - 3$ when $n = 7$

Write the original expression: $2(n + 5) - 3$ = Ready to substitute

Replace $n$ with $7$: $2(7 + 5) - 3$ = Substitution complete

Solve inside parentheses first: $2(12) - 3$ = $7 + 5 = 12$

Multiply: $24 - 3$ = $2 \times 12 = 24$

Subtract to get the final answer: $24 - 3 = 21$ = $21$

Answer: When $n = 7$, the expression $2(n + 5) - 3$ equals $21$

Mistake: Forgetting to multiply: Writing $2x$ as $25$ when $x = 5$ instead of $2 \times 5 = 10$

Why: The coefficient and variable are being multiplied, even though the multiplication sign is not written.

Correct: $2x$ means $2 \times x$. When $x = 5$: $2x = 2 \times 5 = 10$

Mistake: Wrong order of operations: Doing $3 + 2 \times 4 = 20$ instead of $3 + 8 = 11$

Why: Addition was done before multiplication. Remember PEMDAS: Multiplication comes before Addition.

Correct: Multiply first: $3 + 2 \times 4 = 3 + 8 = 11$

Mistake: Substituting in the wrong place: For $2x + y$ with $x = 3$, $y = 4$, writing $23 + 4$

Why: The number was placed next to the variable as digits rather than multiplying.

Correct: $2x + y = 2(3) + 4 = 6 + 4 = 10$

Calculating Costs

Businesses use expressions to calculate prices based on quantity.

A taxi charges a 3 euro base fare plus 2 euros per kilometer. The expression $3 + 2k$ gives the total cost for $k$ kilometers.

Temperature Conversion

Scientists convert between Celsius and Fahrenheit using formulas.

To convert Celsius to Fahrenheit, use $F = \frac{9}{5}C + 32$. For $C = 20°$: $F = \frac{9}{5}(20) + 32 = 36 + 32 = 68°$

Q: Why do we use parentheses when substituting?

A: Parentheses make the substitution clear and prevent mistakes. For $3x$ with $x = 5$, writing $3(5)$ clearly shows multiplication, whereas $35$ looks like thirty-five.

Q: What if I get a negative answer?

A: Negative answers are completely valid! For example, $x - 10$ when $x = 3$ gives $3 - 10 = -7$. Just follow the operations correctly.

Q: Does it matter which variable I substitute first?

A: No, you can substitute variables in any order. Just make sure to replace ALL occurrences of each variable with its given value.