QUESTION IMAGE
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 $5x - 7.4 = 7.6$
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 $8 + \frac{x}{3} = 13$:
- Subtract 8: $\frac{x}{3} = 5$
- Multiply by 3: $x = 15$ (matches handwritten))
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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 $8 + \frac{x}{3} = 13$:
- Subtract 8: $\frac{x}{3} = 5$
- Multiply by 3: $x = 15$ (matches handwritten))