Linear Equations — Algebra I 練習ワークシート

Grades 8–9 かんたん 10問

A linear equation in one variable has the form $ax + b = c$ , where the variable appears only to the first power. Solving means finding the value of the variable that makes the equation true.

The golden rule of equation solving is balance: whatever you do to one side, do to the other. Work in reverse order of operations — undo addition/subtraction first, then multiplication/division.

When variables appear on both sides, collect them on one side and constants on the other. Always check your answer by substituting into the original equation.

練習するスキル

One-step and two-step equations
Equations with variables on both sides
Distributive property in equations
Checking solutions

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練習ワークシート：Linear Equations

指示： 各問題を丁寧に解きましょう。途中式もはっきりと書きましょう。最終的な答えは、指定された場所または指示に従って別の用紙に書いてください。

1.Solve for $x$ : $3x + 7 = 22$ .

Linear Equations — 練習ワークシート（続き）

2.Solve for $y$ : $5y - 9 = 2y + 6$ .
3.Solve for $a$ : $4(a - 3) = 2a + 8$ .

Linear Equations — 練習ワークシート（続き）

4.Solve for $b$ : $\dfrac{b}{5} + 2 = 7$ .
5.Solve for $c$ : $6c + 4 = 2c - 12$ .

Linear Equations — 練習ワークシート（続き）

6.A number increased by 9 is equal to 24. Find the number.
7.The sum of twice a number and 5 is 19. What is the number?

Linear Equations — 練習ワークシート（続き）

8.Three times a number, minus 4, is equal to 11. Find the number.
9.A rectangle has a length that is 3 inches more than its width. The perimeter is 30 inches. Find the width and length.

Linear Equations — 練習ワークシート（続き）

10.Tickets to a play cost $8 for adults and $5 for children. A group of 12 people paid $78 total. How many adults and how many children were in the group?

解答集

1.

Subtract 7: $3x = 15$ ; Divide by 3: $x = 5$

最終回答： $x = 5$
2.

Subtract $2y$ : $3y - 9 = 6$ ; Add 9: $3y = 15$ ; Divide by 3: $y = 5$

最終回答： $y = 5$
3.

Distribute: $4a - 12 = 2a + 8$ ; Subtract $2a$ : $2a - 12 = 8$ ; Add 12: $2a = 20$ ; Divide by 2: $a = 10$

最終回答： $a = 10$
4.

Subtract 2: $\dfrac{b}{5} = 5$ ; Multiply by 5: $b = 25$

最終回答： $b = 25$
5.

Subtract $2c$ : $4c + 4 = -12$ ; Subtract 4: $4c = -16$ ; Divide by 4: $c = -4$

最終回答： $c = -4$
6.

Let $n$ be the number. $n + 9 = 24$ ; Subtract 9: $n = 15$

最終回答： The number is 15.

解答集（続き）

7.

Let $n$ be the number. $2n + 5 = 19$ ; Subtract 5: $2n = 14$ ; Divide by 2: $n = 7$

最終回答： The number is 7.
8.

Let $n$ be the number. $3n - 4 = 11$ ; Add 4: $3n = 15$ ; Divide by 3: $n = 5$

最終回答： The number is 5.
9.

Let $w$ be the width. Then length $= w + 3$ . Perimeter: $2w + 2(w + 3) = 30$ ; Simplify: $4w + 6 = 30$ ; Subtract 6: $4w = 24$ ; Divide by 4: $w = 6$ ; Length: $6 + 3 = 9$

最終回答： Width = 6 inches, Length = 9 inches.
10.

Let $a$ be number of adults, $c$ be number of children. $a + c = 12$ ; $8a + 5c = 78$ ; From first: $c = 12 - a$ ; Substitute: $8a + 5(12 - a) = 78$ ; $3a + 60 = 78$ ; Subtract 60: $3a = 18$ ; Divide by 3: $a = 6$ ; Then $c = 12 - 6 = 6$

最終回答： 6 adults and 6 children.

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避けるべきよくある間違い

Sign errors when moving terms across the equals sign
Dividing only one term instead of the entire side
Forgetting to distribute to every term inside parentheses
Accepting extraneous solutions without checking

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