Grade 7 Math: Adding, Subtracting, and Simplifying Linear Expressions

Flashcards created from 7th grade math sources covering algebraic expression simplification, linear vs non-linear expressions, additive inverses, and methods for adding and subtracting linear expressions.

What is a linear expression?

An algebraic expression in which the exponent of any variable in that expression is only $1$.

Why are expressions such as $6x^3$ and $3x^2 + 4x - 5$ classified as nonlinear?

Because they contain variable terms with exponents other than $1$, such as exponents $3$ and $2$.

Why is a constant value like $8$ or $9$ considered a linear expression?

All constants are linear in nature because a constant can be thought of as having a term $0 \times x$ with variable exponent $1$, and its graph forms a straight line.

What are additive inverses in mathematics?

Two expressions or numbers that have a sum of $0$. Multiplying any value or expression by $-1$ yields its additive inverse.

How do you find the additive inverse of a multi-term linear expression?

Multiply the entire linear expression by $-1$ by distributing $-1$ to every term inside the expression.

What is the additive inverse of the linear expression $3x - 8$?

$$-3x + 8$$

What is the additive inverse of the linear expression $6x - 3$?

$$-6x + 3$$

What is the equivalent expression in simplest form for $3x + 5x - 2$?

$$8x - 2$$

What is the equivalent expression in simplest form for $2(-4x + 1)$?

$$-8x + 2$$

What is the equivalent expression in simplest form for $-4(2x - 1)$?

$$-8x + 4$$

What is the equivalent expression in simplest form for $-4(-2x + 1)$?

$$8x - 4$$

What are the four steps to subtract linear expressions using algebra tiles?

1. Rewrite as addition by finding the additive inverse of the second expression. 2. Model the linear expressions using algebra tiles. 3. Remove any zero pairs. 4. Write a linear expression that represents the remaining algebra tiles.

What is the result when you simplify $(5x - 3) - (2x + 2)$ using algebra tiles?

$$3x - 5$$

What is the result when you simplify $(-2x - 3) - (5x - 4)$ using algebra tiles?

$$-7x + 1$$

What are the three steps to subtract linear expressions by stacking like terms?

1. Rewrite as addition using the additive inverse. 2. Stack like terms in columns. 3. Add like terms and simplify if necessary.

What is the difference when subtracting $(7x - 6) - (4x + 3)$ by stacking like terms?

$$3x - 9$$

What is the difference when subtracting $(-4x - 9) - (2x + 6)$ by stacking like terms?

$$-6x - 15$$

What is the difference when subtracting $(\frac{1}{2}x + \frac{2}{3}) - (\frac{3}{4}x - \frac{1}{6})$?

$$-\frac{1}{4}x + \frac{5}{6}$$

What is the difference when subtracting $(\frac{4}{9}x - \frac{5}{6}) - (\frac{1}{3}x - \frac{1}{2})$?

$$\frac{1}{9}x - \frac{1}{3}$$

Leah's distance is represented by $3x + 1.2\,\text{miles}$ and Andre's distance is represented by $5x + 0.4\,\text{miles}$. What expression represents how many fewer miles Leah traveled compared to Andre?

$$2x - 0.8\,\text{miles}$$

Maya streams $2.4x + 5\,\text{hours}$ and Jordan streams $1.8x + 6.5\,\text{hours}$. What expression represents how many more hours Maya streamed than Jordan?

$$0.6x - 1.5\,\text{hours}$$

What are the three steps to add linear expressions using algebra tiles?

1. Model the linear expressions using algebra tiles. 2. Remove any zero pairs. 3. Write a linear expression representing the remaining tiles.

What is the sum of $(4x - 1) + (-3x - 2)$ using algebra tiles?

$$x - 3$$

What is the sum of $(-2x + 3) + (x - 4)$ using algebra tiles?

$$-x - 1$$

What are the three steps to add linear expressions by stacking like terms?

1. If necessary, rewrite the linear expression using addition. 2. Stack like terms in columns. 3. Add like terms and simplify if necessary.

What is the sum of $(-9x - 4) + (4x - 5)$ in simplest form?

$$-5x - 9$$

What is the sum of $(7x - 3) + (-9x - 1)$ in simplest form?

$$-2x - 4$$

What is the sum of $(\frac{1}{4}x + 3) + (\frac{3}{8}x - 5)$ in simplest form?

$$\frac{5}{8}x - 2$$

What is the sum of $(\frac{7}{3}x - 9) + (-\frac{5}{6}x - 2)$ in simplest form?

$$\frac{3}{2}x - 11$$

A bike shop spends $2.5b + 5\,\text{hours}$ on road bikes and $3.25b + 1.25\,\text{hours}$ on mountain bikes. What simplified expression represents the total hours needed to prepare for the sale?

$$5.75b + 6.25\,\text{hours}$$

Tent 1 costs $45.50x + 150$ dollars and Tent 2 costs $60.25x + 80$ dollars. What simplified linear algebraic expression represents the total cost for renting both tents for $x$ hours?

$105.75x + 230$ dollars