Question

date: 2/11/26 block: 3rd
pws 2.11 - shamrockin equations
copy and solve each equation on column 1 of paper. be sure to show all the required steps like we have practiced in class. after you complete all 10 problems, you may work with a partner who has completed column 2. match your answers to determine the color pattern for the shamrocks. if your answers dont match, redo the problems. color, staple your work, and these questions together. turn in.
column 1

1. $13x + 7 = 8x + 27$
2. $2x - 1 = 7x + 44$
3. $-5x + 2 = 10 - 9x$
4. $2(4x - 3) = 4x - 78$
5. $12 - 9x = -3(x + 10)$
6. $8x - 2(x + 9) = x + 47$

Explanation:

Problem 1: $13x + 7 = 8x + 27$

Step1: Subtract $8x$ from both sides

$13x - 8x + 7 = 8x - 8x + 27$
$5x + 7 = 27$

Step2: Subtract 7 from both sides

$5x + 7 - 7 = 27 - 7$
$5x = 20$

Step3: Divide by 5 on both sides

$\frac{5x}{5} = \frac{20}{5}$
$x = 4$

Problem 2: $2x - 1 = 7x + 44$

Step1: Subtract $2x$ from both sides

$2x - 2x - 1 = 7x - 2x + 44$
$-1 = 5x + 44$

Step2: Subtract 44 from both sides

$-1 - 44 = 5x + 44 - 44$
$-45 = 5x$

Step3: Divide by 5 on both sides

$\frac{-45}{5} = \frac{5x}{5}$
$x = -9$

Problem 3: $-5x + 2 = 10 - 9x$

Step1: Add $9x$ to both sides

$-5x + 9x + 2 = 10 - 9x + 9x$
$4x + 2 = 10$

Step2: Subtract 2 from both sides

$4x + 2 - 2 = 10 - 2$
$4x = 8$

Step3: Divide by 4 on both sides

$\frac{4x}{4} = \frac{8}{4}$
$x = 2$

Problem 4: $2(4x - 3) = 4x - 78$

Step1: Expand left side via distributive property

$2\times4x - 2\times3 = 4x - 78$
$8x - 6 = 4x - 78$

Step2: Subtract $4x$ from both sides

$8x - 4x - 6 = 4x - 4x - 78$
$4x - 6 = -78$

Step3: Add 6 to both sides

$4x - 6 + 6 = -78 + 6$
$4x = -72$

Step4: Divide by 4 on both sides

$\frac{4x}{4} = \frac{-72}{4}$
$x = -18$

Problem 5: $12 - 9x = -3(x + 10)$

Step1: Expand right side via distributive property

$12 - 9x = -3x - 3\times10$
$12 - 9x = -3x - 30$

Step2: Add $9x$ to both sides

$12 - 9x + 9x = -3x + 9x - 30$
$12 = 6x - 30$

Step3: Add 30 to both sides

$12 + 30 = 6x - 30 + 30$
$42 = 6x$

Step4: Divide by 6 on both sides

$\frac{42}{6} = \frac{6x}{6}$
$x = 7$

Problem 6: $8x - 2(x + 9) = x + 47$

Step1: Expand left side via distributive property

$8x - 2x - 2\times9 = x + 47$
$6x - 18 = x + 47$

Step2: Subtract $x$ from both sides

$6x - x - 18 = x - x + 47$
$5x - 18 = 47$

Step3: Add 18 to both sides

$5x - 18 + 18 = 47 + 18$
$5x = 65$

Step4: Divide by 5 on both sides

$\frac{5x}{5} = \frac{65}{5}$
$x = 13$

Answer:

1. $x=4$
2. $x=-9$
3. $x=2$
4. $x=-18$
5. $x=7$
6. $x=13$