Question

extended practicegeneration geniusintro to algebraic expressions1. circle each of the terms in the expression.$2x + 3y + 10 - x - 2y - 4$2. circle each expression and box each equation.5 $3x$ $5 + 7 = 20 - 8$ $y + 7$ $5 + 10 =$ $35 + 14 =$3. identify the coefficients, constants, and variables in the expression $5x + 8y + 7 - 3x - y + 9$.identify the like terms in each expression:a. $10 + 3x + 5 - x$b. $5c + 3d + 11c - 3$simplify each expression.a. $8x + 4x + 5 - 2$b. $5y + 10 + 9y - 2x$simplify each expression.a. $5x + 10 - x + 7$b. $18a + 6m + 9 - 13a - 3m + 11$which expression has more terms? explain how you know.$a + 2b + 3c + 4d + 5$

Explanation:

Step1: Identify terms in $2x+3y+10-x-2y-4$

Terms are separated by $+$/$-$: $2x$, $3y$, $10$, $-x$, $-2y$, $-4$

Step2: Classify expressions/equations

Expressions (no $=$): $5$, $3x$, $y+7$; Equations (has $=$): $5+7=20-8$, $5+10=$, $35+14=$

Step3: Identify components of $5x+8y+7-3x-y+9$

Coefficients: $5, 8, -3, -1$; Constants: $7, 9$; Variables: $x, y$

Step4: Find like terms (a)

In $10+3x+5-x$: constant terms $10,5$; $x$-terms $3x,-x$

Step5: Find like terms (b)

In $5c+3d+11c-3$: $c$-terms $5c,11c$; constant $-3$; $d$-term $3d$

Step6: Simplify expression (a)

Combine like terms: $8x+4x+5-2=(8+4)x+(5-2)=12x+3$

Step7: Simplify expression (b)

Combine like terms: $5y+10+9y-2x=(5+9)y-2x+10=14y-2x+10$

Step8: Simplify expression (a)

Combine like terms: $5x+10-x+7=(5-1)x+(10+7)=4x+17$

Step9: Simplify expression (b)

Combine like terms: $18a+6m+9-13a-3m+11=(18-13)a+(6-3)m+(9+11)=5a+3m+20$

Step10: Count terms in $a+2b+3c+4d+5$

Terms: $a, 2b, 3c, 4d, 5$ (5 total; no comparison expression provided, so count given terms)

Answer:

1. Terms: $\boldsymbol{2x}$, $\boldsymbol{3y}$, $\boldsymbol{10}$, $\boldsymbol{-x}$, $\boldsymbol{-2y}$, $\boldsymbol{-4}$ (each is a separate term to circle)
2. Circled expressions: $\boldsymbol{5}$, $\boldsymbol{3x}$, $\boldsymbol{y+7}$; Boxed equations: $\boldsymbol{5+7=20-8}$, $\boldsymbol{5+10=}$, $\boldsymbol{35+14=}$
3. Coefficients: $\boldsymbol{5, 8, -3, -1}$; Constants: $\boldsymbol{7, 9}$; Variables: $\boldsymbol{x, y}$
4. a. Like terms: $\boldsymbol{10 \text{ and } 5}$, $\boldsymbol{3x \text{ and } -x}$

b. Like terms: $\boldsymbol{5c \text{ and } 11c}$

1. a. $\boldsymbol{12x + 3}$

b. $\boldsymbol{14y - 2x + 10}$

1. a. $\boldsymbol{4x + 17}$

b. $\boldsymbol{5a + 3m + 20}$

1. The expression $\boldsymbol{a+2b+3c+4d+5}$ has 5 terms (each part separated by $+$ is a term: $a$, $2b$, $3c$, $4d$, $5$; no second expression provided to compare, so this is the term count for the given expression)