Question

solve the equation:
\\(\frac{x}{2} - 3 = 17\\)

circle the common factors of
-16m and 20mn.

2, 2m, 4mn, 4,
m, 8n, 4m, 12n

students planted 4(2x + 3y)
amount of trees on saturday
and then 3(5x + 4) amount of
trees on sunday. what is the
total amount of trees that the
students planted?

solve:
\\(\frac{k}{7} + 3 - 2k = -3\\)

Explanation:

Step1: Isolate $\frac{x}{2}$

Add 3 to both sides:
$\frac{x}{2}=17+3$
$\frac{x}{2}=20$

Step2: Solve for $x$

Multiply both sides by 2:
$x=20\times2$
$x=40$

Step1: Factor 16m

$16m=2\times2\times2\times2\times m$

Step2: Factor 20mn

$20mn=2\times2\times5\times m\times n$

Step3: Identify common factors

Common factors: 2, 4, $m$, $2m$, $4m$

Step1: Expand Saturday's tree count

$4(2x+3y)=8x+12y$

Step2: Expand Sunday's tree count

$3(5x+4)=15x+12$

Step3: Sum the two expressions

$(8x+12y)+(15x+12)=23x+12y+12$

Step1: Eliminate denominator

Multiply all terms by 7:
$k+21-14k=-21$

Step2: Combine like terms

$-13k+21=-21$

Step3: Isolate $-13k$

Subtract 21 from both sides:
$-13k=-21-21$
$-13k=-42$

Step4: Solve for $k$

Divide by -13:
$k=\frac{-42}{-13}=\frac{42}{13}$

Answer:

1. $x=40$
2. 2, 4, $m$, $2m$, $4m$
3. $23x + 12y + 12$
4. $k=\frac{42}{13}$