Question

date ____ pd ____
erent math cards. solve for x on each card and record the
= 18
c $\frac{x}{7}+ 5 = 8$
d $37 = 32 + \frac{x}{10}$
g $5x + 27 = 32$
h $2x - 8.7 = 21.3$
$+ \frac{x}{3} = 13$
l $8x - 2.5 = 5.5$

• 10

p $5x - 7.4 = 7.6$

Explanation:

Let's solve each equation step by step:

Card C: $\boldsymbol{\frac{x}{7} + 5 = 8}$

Step1: Subtract 5 from both sides

$\frac{x}{7} + 5 - 5 = 8 - 5$
$\frac{x}{7} = 3$

Step2: Multiply both sides by 7

$\frac{x}{7} \times 7 = 3 \times 7$
$x = 21$

Card D: $\boldsymbol{37 = 32 + \frac{x}{10}}$

Step1: Subtract 32 from both sides

$37 - 32 = 32 - 32 + \frac{x}{10}$
$5 = \frac{x}{10}$

Step2: Multiply both sides by 10

$5 \times 10 = \frac{x}{10} \times 10$
$x = 50$

Card G: $\boldsymbol{5x + 27 = 32}$

Step1: Subtract 27 from both sides

$5x + 27 - 27 = 32 - 27$
$5x = 5$

Step2: Divide both sides by 5

$\frac{5x}{5} = \frac{5}{5}$
$x = 1$

Card H: $\boldsymbol{2x - 8.7 = 21.3}$

Step1: Add 8.7 to both sides

$2x - 8.7 + 8.7 = 21.3 + 8.7$
$2x = 30$

Step2: Divide both sides by 2

$\frac{2x}{2} = \frac{30}{2}$
$x = 15$ (Note: The handwritten answer here was incorrect; correct is 15, not 13)

Card L: $\boldsymbol{8x - 2.5 = 5.5}$

Step1: Add 2.5 to both sides

$8x - 2.5 + 2.5 = 5.5 + 2.5$
$8x = 8$

Step2: Divide both sides by 8

$\frac{8x}{8} = \frac{8}{8}$
$x = 1$

Card P: $\boldsymbol{5x - 7.4 = 7.6}$

Step1: Add 7.4 to both sides

$5x - 7.4 + 7.4 = 7.6 + 7.4$
$5x = 15$

Step2: Divide both sides by 5

$\frac{5x}{5} = \frac{15}{5}$
$x = 3$

Summary of Correct Answers:

• Card C: $x = 21$
• Card D: $x = 50$
• Card G: $x = 1$
• Card H: $x = 15$ (corrected)
• Card L: $x = 1$
• Card P: $x = 3$

(Note: For the partially visible card with $\boldsymbol{+\frac{x}{3} = 13}$ and handwritten $=15$, assuming the left term is 8 (common structure), solving $8 + \frac{x}{3} = 13$:

1. Subtract 8: $\frac{x}{3} = 5$
2. Multiply by 3: $x = 15$ (matches handwritten))

Answer:

Let's solve each equation step by step:

Card C: $\boldsymbol{\frac{x}{7} + 5 = 8}$

Step1: Subtract 5 from both sides

$\frac{x}{7} + 5 - 5 = 8 - 5$
$\frac{x}{7} = 3$

Step2: Multiply both sides by 7

$\frac{x}{7} \times 7 = 3 \times 7$
$x = 21$

Card D: $\boldsymbol{37 = 32 + \frac{x}{10}}$

Step1: Subtract 32 from both sides

$37 - 32 = 32 - 32 + \frac{x}{10}$
$5 = \frac{x}{10}$

Step2: Multiply both sides by 10

$5 \times 10 = \frac{x}{10} \times 10$
$x = 50$

Card G: $\boldsymbol{5x + 27 = 32}$

Step1: Subtract 27 from both sides

$5x + 27 - 27 = 32 - 27$
$5x = 5$

Step2: Divide both sides by 5

$\frac{5x}{5} = \frac{5}{5}$
$x = 1$

Card H: $\boldsymbol{2x - 8.7 = 21.3}$

Step1: Add 8.7 to both sides

$2x - 8.7 + 8.7 = 21.3 + 8.7$
$2x = 30$

Step2: Divide both sides by 2

$\frac{2x}{2} = \frac{30}{2}$
$x = 15$ (Note: The handwritten answer here was incorrect; correct is 15, not 13)

Card L: $\boldsymbol{8x - 2.5 = 5.5}$

Step1: Add 2.5 to both sides

$8x - 2.5 + 2.5 = 5.5 + 2.5$
$8x = 8$

Step2: Divide both sides by 8

$\frac{8x}{8} = \frac{8}{8}$
$x = 1$

Card P: $\boldsymbol{5x - 7.4 = 7.6}$

Step1: Add 7.4 to both sides

$5x - 7.4 + 7.4 = 7.6 + 7.4$
$5x = 15$

Step2: Divide both sides by 5

$\frac{5x}{5} = \frac{15}{5}$
$x = 3$

Summary of Correct Answers:

• Card C: $x = 21$
• Card D: $x = 50$
• Card G: $x = 1$
• Card H: $x = 15$ (corrected)
• Card L: $x = 1$
• Card P: $x = 3$

(Note: For the partially visible card with $\boldsymbol{+\frac{x}{3} = 13}$ and handwritten $=15$, assuming the left term is 8 (common structure), solving $8 + \frac{x}{3} = 13$:

1. Subtract 8: $\frac{x}{3} = 5$
2. Multiply by 3: $x = 15$ (matches handwritten))