This section is dedicated to the foundational skill of constructing algebraic expressions and equations, pivotal for solving a wide range of algebraic problems.

**Constructing Algebraic Expressions**

Algebraic expressions represent quantities and their relationships without an equality sign. The construction process involves identifying variables and applying operations as described in scenarios or word problems.

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**Example 1: Constructing an Expression for a Rectangle's Length**

**Given:** A rectangle's length is 5 units more than its width, $w$.

**Construct the expression:**

- Length expression: $w + 5$

**Example 2: Expression from a Scenario**

**Given:** Triple a number decreased by 7.

**Construct the expression:**

- Expression: $3x - 7$

**Constructing Algebraic Equations**

Equations set two expressions equal to each other, allowing for the representation of scenarios where quantities are related through an exact balance.

**Example 1: Equating an Expression to a Value**

**Given:** The sum of three times a number and 11 equals 44.

**Construct the equation:**

- Equation: $3x + 11 = 44$

**Example 2: Word Problem to Equation**

**Given:** Twice the difference of a number and 5 equals the number increased by 3.

**Construct the equation:**

- Equation: $2(x - 5) = x + 3$

**Practice Problems**

**Problem 1: Expression Construction**

**Given:** Five less than four times a number.

**Construct the expression:**

- Expression: $4x - 5$

**Problem 2: Equation Construction**

**Given:** The product of a number and 7 equals 21.

**Construct the equation:**

- Equation: $7x = 21$

**Problem 3: From Word Problem to Equation**

**Given:** The perimeter of a rectangle is twice the sum of its length $(l)$ and width $(w)$. Express the perimeter $(P)$ in terms of $l$ and $w$.

**Construct the equation:**

- Perimeter equation: $P = 2(l + w)$