This page is designed to help students, parents, and teachers master the topic of algebraic expressions through carefully selected questions and step-by-step solutions with explanations. Each solution goes beyond providing the final answer by explaining the reasoning behind every step, helping learners build a strong foundation in algebra. Since algebraic expressions are one of the most essential concepts in understanding algebra, it is crucial to study them thoroughly to succeed in more advanced mathematics.
The questions on this page cover essential topics related to algebraic expressions, including:
Which of the following is an algebraic expression?
What is the coefficient of the term in \(x\) in the following expressions?
Find the value of \(2x + 7\) for the given values of \(x\).
Find the value of \(\dfrac{x}{3} - 9\) for the given values of \(x\).
Find the value of \(\dfrac{-x + 2}{2} + 1\) for the given values of \(x\).
Find the value of \(12x - 3\) for the given values of \(x\).
Find the value of \(-0.1x + 2.5\) for the given values of \(x\).
Which of the following expressions has the largest value when \(x = -3\)?
Which of the following shows the commutative property?
Which of the following shows the associative property?
Which of the following is equivalent to \(3x + 2 - x + 4\)?
Which expression represents the statement: “Two times x plus 20”?
Which expression matches the statement: “Three times x subtracted from 17”?
Jo has \(x\) cards. Janette has 10 more. Write an expression for Janette’s cards.
Carla had 20 toy cars. She lost \(x\). Write an expression for her remaining cars.
Chris had \$200. He spent \$20 on food and bought a book for \(a\) dollars. How much does he have left?
Nathan had \(x\) cards. He gave half to Tanya, and Tanya gave one-third of her cards to Salma. Write an expression for how many cards Tanya has.
Algebraic expressions contain real numbers, variables, and the four basic operations: \(+, -, \times, \div\).
Examples:
\[ 2x + 2, \quad \dfrac{x}{2} + 6 - x, \quad \dfrac{x+3}{2}, \quad -\dfrac{x}{8} \]Note: \(2x\) means \(2 \times x\).
Non-examples:
The coefficient of a term is the real number multiplying the variable.
| Expression | Term in \(x\) | Written as Multiplication | Coefficient |
|---|---|---|---|
| \(2x - 7\) | \(2x\) | \(2 \times x\) | 2 |
| \(\dfrac{x}{2} - 10\) | \(\dfrac{x}{2}\) | \(\dfrac{1}{2} \times x\) | \(\dfrac{1}{2}\) |
| \(-x + 7\) | \(-x\) | \(-1 \times x\) | -1 |
| \(x + 7\) | \(x\) | \(1 \times x\) | 1 |
| \(-\dfrac{x}{4}\) | \(-\dfrac{x}{4}\) | \(-\dfrac{1}{4} \times x\) | \(-\dfrac{1}{4}\) |
Substitute the value of \(x\) and simplify.
| Expression | Value of \(x\) | Substitution | Result |
|---|---|---|---|
| \(2x+7\) | -1 | \(2(-1)+7\) | 5 |
| \(2x+7\) | -4 | \(2(-4)+7\) | -1 |
| \(2x+7\) | 0 | \(2(0)+7\) | 7 |
| \(2x+7\) | 5 | \(2(5)+7\) | 17 |
| Expression | Value of \(x\) | Substitution | Result |
|---|---|---|---|
| \(\dfrac{x}{3}-9\) | 0 | \(\dfrac{0}{3}-9\) | -9 |
| \(\dfrac{x}{3}-9\) | 3 | \(\dfrac{3}{3}-9\) | -8 |
| \(\dfrac{x}{3}-9\) | 9 | \(\dfrac{9}{3}-9\) | -6 |
| \(\dfrac{x}{3}-9\) | -12 | \(\dfrac{-12}{3}-9\) | -13 |
| Expression | Value of \(x\) | Substitution | Result |
|---|---|---|---|
| \(\dfrac{-x+2}{2}+1\) | 0 | \(\dfrac{-0+2}{2}+1\) | 2 |
| \(\dfrac{-x+2}{2}+1\) | 2 | \(\dfrac{-2+2}{2}+1\) | 1 |
| \(\dfrac{-x+2}{2}+1\) | -2 | \(\dfrac{2+2}{2}+1\) | 3 |
| \(\dfrac{-x+2}{2}+1\) | -12 | \(\dfrac{12+2}{2}+1\) | 8 |
| Expression | Value of \(x\) | Substitution | Result |
|---|---|---|---|
| \(12x-3\) | \(\dfrac{1}{2}\) | \(12(\dfrac{1}{2})-3\) | 3 |
| \(12x-3\) | \(\dfrac{1}{6}\) | \(12(\dfrac{1}{6})-3\) | -1 |
| \(12x-3\) | \(-\dfrac{3}{4}\) | \(12(-\dfrac{3}{4})-3\) | -12 |
| \(12x-3\) | \(-\dfrac{1}{4}\) | \(12(-\dfrac{1}{4})-3\) | -6 |
| Expression | Value of \(x\) | Substitution | Result |
|---|---|---|---|
| \(-0.1x+2.5\) | 1 | \(-0.1(1)+2.5\) | 2.4 |
| \(-0.1x+2.5\) | -1 | \(-0.1(-1)+2.5\) | 2.6 |
| \(-0.1x+2.5\) | 2 | \(-0.1(2)+2.5\) | 2.3 |
| \(-0.1x+2.5\) | -2 | \(-0.1(-2)+2.5\) | 2.7 |
For \(x=-3\):
| Expression | Value |
|---|---|
| \(x+10\) | 7 |
| \(-x+10\) | 13 |
| \(\dfrac{x}{3}+10\) | 9 |
| \(-\dfrac{x}{3}+10\) | 11 |
Largest value: \(-x+10=13\) when \(x=-3\).
The commutative property of addition:
\[ a+b=b+a \]The associative property of addition:
\[ a+(b+c)=(a+b)+c \]Simplify by combining like terms:
\[ 3x+2-x+4=3x-x+2+4=2x+6 \]So \(3x+2-x+4\) is equivalent to \(2x+6\).
“Two times \(x\) plus 20”:
\[ 2 \times x + 20 = 2x+20 \]“Three times \(x\) subtracted from 17”:
\[ 17 - 3x \]If Jo has \(x\) cards, Janette has:
\[ x+10 \]Carla starts with 20 toy cars and loses \(x\):
\[ 20-x \]Chris starts with \$200. After spending \$20 on food and \(a\) on books:
\[ 200-20-a \]Nathan has \(x\) cards.