Comprehensive Guide to One-Step Equations and Variable Isolation

Mathematical Exercise Fragments and Overview

The primary focus is on solving one-step equations to find the value of a given variable, with instructions to write the final answers in their simplest form. Beyond the structured problem set, various numerical fragments and instructions are present. This includes tasks to find the sum of given values, specifically mentioning numbers such as $121$ and $422$.

Additional fragments noted include sequence markers and operations such as $5$. $\frac{3}{31/2}$, $5$. पंडे $12$, and $9.3$ followed by the characters 름날 and the number $90$. Other isolated notations include $3$봉, $+9$, and a collection of digit sequences: $7$, $11$, $13.$, $84$, $72$, $17.$, $21.$, $5$, $11$, and $14$.

Single-Step Equations: Problems 81 Through 85

Problem 81 involves the addition equation $x + 18 = 32$. To isolate the variable, the inverse operation of subtraction is performed: $32 - 18 = 14$, resulting in the solution $x = 14$.

Problem 82 presents a multiplication equation $18f = 720$. Dividing both sides by the coefficient of the variable leads to the calculation $720 \div 18 = 40$. The solved value for the variable is $f = 40$.

Problem 83 requires solving the subtraction equation $h - 56 = 57$. By applying the inverse operation of addition, the value of the variable is determined through the calculation $56 + 57 = 113$. Thus, $h = 113$.

Problem 84 consists of the division equation $\frac{b}{6} = 12$. To solve for $b$, multiplication is used: $12 \times 6 = 72$. The final value determined for the variable is $b = 72$.

Problem 85 is listed with the terms $12r$ and $76$. The solution process involves the addition operation $76 + 12 = 88$, which yields the result $y = 88$.

Single-Step Equations: Problems 86 Through 90

Problem 86 features the addition equation $33 + d = 65$. Subtracting the constant from both sides gives $65 - 33 = 32$. Consequently, the variable $d = 32$.

Problem 87 is the multiplication equation $14m = 42$. The variable is isolated by dividing the product by the coefficient: $42 \div 14 = 3$. The solution is $m = 3$.

Problem 88 is presented as $10c = 5$. The transcript records the operation as $5 \div 10 = 2$, leading to the conclusion $c = 2$.

Problem 89 shows the equation $38 = 19j$. This is solved by determining that $38$ is the product of $19 \times 2$. Therefore, the variable $j = 2$.

Problem 90 involves the addition equation $w + 65 = 100$. The value of $w$ is found through the subtraction $100 - 65 = 35$. The result is $w = 35$.

Single-Step Equations: Problems 91 Through 95

Problem 91 is documented as $r \, 7 \, 9$. The solution provided involves adding the terms $7 + 9 = 16$, resulting in the variable assignment $y = 16$.

Problem 92 is written as $x + 12 = 9$, though the subsequent calculations show $9 \times 12 = 108$. There is a further notation of $108 \, 4 = 108$ and the word Seven.

Problem 93 contains the equation $14 + x = 18$. By subtracting $14$ from $18$, the calculation $18 - 14 = 4$ is performed, yielding $x = 4$.

Problem 94 involves an equation represented as $\frac{p}{22} = 7$. The variable is solved by performing the multiplication $22 \times 7 = 154$. The final value for the variable is $p = 154$.

Problem 95 presents the equation $47 = x - 5$. Adding $5$ to both sides of the equation results in the sum $47 + 5 = 52$. Thus, the variable $x = 52$.

Single-Step Equations: Problems 96 Through 100

Problem 96 presents the addition equation $k + 16 = 76$. Solving for the variable requires subtracting $16$ from $76$, which yields $76 - 16 = 60$. Therefore, $k = 60$.

Problem 97 involves the equation $2 = 6m$. The operation is identified as $2 \div 6$, which results in the variable value $m = \frac{1}{3}$.

Problem 98 is the subtraction equation $t - 8 = 14$. To find the value of $t$, the constant $8$ is added to $14$ to get $14 + 8 = 22$. The final answer is $t = 22$, while a secondary notation mentions $7 = 88$.

Problem 99 uses a division equation represented by $\frac{h}{19} = 11$. Multiplying the divisor by the quotient, $19 \times 11$, results in the value $209$. Thus, $h = 209$.

Problem 100 consists of the equation $47 = 18 + b$. To isolate the variable $b$, the calculation $47 - 18 = 29$ is carried out. The solution is $b = 29$.

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