Question

date:
solving equations
holiday color by number
directions: solve the equations or inequalities. find the color that corresponds to the correct answer in the table on
the next page and write it in the space provided in each section. color the christmas sweater using the colors noted
for each question number. for example, if question number 1 is dark green, color all the #1s in the picture dark
green.
1.
$11x - 9 = 13 - 5x$
$x=\frac{11}{8}=1.375$
color: brown
2.
image of a balance scale with x, x, 1 on left and x, x, 1,1,1,1,1 on right
color:
3.
$7x + 9 = 3x - 21$
color:
4.
image of two boxes, first with 4 triangles and 9 circles, second with 8 triangles and 3 circles
color:
5.
$\frac{3}{4}x = 18 - \frac{1}{2}x$
color:
6.
$12 + \frac{3}{4}x = 18 + 3x$
color:
7.
$80 - 0.6n = 100 - n$
color:
8.
$3.5x + 2 = 3x +4.5$
color:
9.
$8x - 2 = -9 + 6x$
color:

Explanation:

Step1: Solve \( 11x - 9 = 13 - 5x \)

Add \( 5x \) to both sides: \( 11x + 5x - 9 = 13 \), so \( 16x - 9 = 13 \). Add \( 9 \) to both sides: \( 16x = 13 + 9 = 22 \). Divide by \( 16 \): \( x = \frac{22}{16} = \frac{11}{8} = 1.375 \).

Step2: Solve \( 7x + 9 = 3x - 21 \)

Subtract \( 3x \) from both sides: \( 4x + 9 = -21 \). Subtract \( 9 \): \( 4x = -30 \). Divide by \( 4 \): \( x = -\frac{30}{4} = -7.5 \).

Step3: Solve \( \frac{3}{4}x = 18 - \frac{1}{2}x \)

Add \( \frac{1}{2}x \) to both sides: \( \frac{3}{4}x + \frac{2}{4}x = 18 \), so \( \frac{5}{4}x = 18 \). Multiply by \( \frac{4}{5} \): \( x = 18 \times \frac{4}{5} = \frac{72}{5} = 14.4 \).

Step4: Solve \( 12 + \frac{3}{4}x = 18 + 3x \)

Subtract \( \frac{3}{4}x \) from both sides: \( 12 = 18 + \frac{9}{4}x \). Subtract \( 18 \): \( -6 = \frac{9}{4}x \). Multiply by \( \frac{4}{9} \): \( x = -6 \times \frac{4}{9} = -\frac{8}{3} \approx -2.666... \).

Step5: Solve \( 80 - 0.6n = 100 - n \)

Add \( n \) to both sides: \( 80 + 0.4n = 100 \). Subtract \( 80 \): \( 0.4n = 20 \). Divide by \( 0.4 \): \( n = 50 \).

Step6: Solve \( 3.5x + 2 = 3x + 4.5 \)

Subtract \( 3x \) from both sides: \( 0.5x + 2 = 4.5 \). Subtract \( 2 \): \( 0.5x = 2.5 \). Divide by \( 0.5 \): \( x = 5 \).

Step7: Solve \( 8x - 2 = -9 + 6x \)

Subtract \( 6x \) from both sides: \( 2x - 2 = -9 \). Add \( 2 \): \( 2x = -7 \). Divide by \( 2 \): \( x = -\frac{7}{2} = -3.5 \).

(Note: For the balance (problem 2) and the triangle - circle (problem 4) problems, we assume they are linear equation models. For the balance: Let the weight of \( x \) be \( x \), and the small circle be \( 1 \). Left: \( 3x + 1 \), Right: \( 2x + 4 \). Set equal: \( 3x + 1 = 2x + 4 \), so \( x = 3 \). For the triangle - circle: Let triangle be \( x \), circle be \( 1 \). Left: \( 4x + 9 \), Right: \( 8x + 3 \). Set \( 4x + 9 = 8x + 3 \), so \( 4x = 6 \), \( x = 1.5 \).)

Answer:

s (with solutions for equations):

1. \( x = 1.375 \), Color (depends on table, here solved)
2. \( x = 3 \) (from balance), Color (depends on table)
3. \( x = -7.5 \), Color (depends on table)
4. \( x = 1.5 \) (from triangle - circle), Color (depends on table)
5. \( x = 14.4 \), Color (depends on table)
6. \( x = -\frac{8}{3} \approx -2.67 \), Color (depends on table)
7. \( n = 50 \), Color (depends on table)
8. \( x = 5 \), Color (depends on table)
9. \( x = -3.5 \), Color (depends on table)

(If we just need the solution for one equation, say problem 1: \( x=\frac{11}{8}=1.375 \))