Linear Equations — Algebra I 练习题

Grades 8–9 简单难度 10 道题

A linear equation in one variable has the form ax+b=cax + 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.

练习的技能

  • One-step and two-step equations
  • Equations with variables on both sides
  • Distributive property in equations
  • Checking solutions
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练习题：Linear Equations

说明： 仔细解答每一道题。清晰地展示所有解题过程。在指定位置或按指示在另一张纸上写出最终答案。

  1. 1.Solve for xx: 3x+7=223x + 7 = 22.

Linear Equations — 练习题（续）

  1. 2.Solve for yy: 5y−9=2y+65y - 9 = 2y + 6.
  2. 3.Solve for aa: 4(a−3)=2a+84(a - 3) = 2a + 8.

Linear Equations — 练习题（续）

  1. 4.Solve for bb: b5+2=7\dfrac{b}{5} + 2 = 7.
  2. 5.Solve for cc: 6c+4=2c−126c + 4 = 2c - 12.

Linear Equations — 练习题（续）

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

Linear Equations — 练习题（续）

  1. 8.Three times a number, minus 4, is equal to 11. Find the number.
  2. 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 — 练习题（续）

  1. 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?

参考答案

  1. 1.
    Subtract 7: 3x=153x = 15; Divide by 3: x=5x = 5
    最终答案： x=5x = 5
  2. 2.
    Subtract 2y2y: 3y−9=63y - 9 = 6; Add 9: 3y=153y = 15; Divide by 3: y=5y = 5
    最终答案： y=5y = 5
  3. 3.
    Distribute: 4a−12=2a+84a - 12 = 2a + 8; Subtract 2a2a: 2a−12=82a - 12 = 8; Add 12: 2a=202a = 20; Divide by 2: a=10a = 10
    最终答案： a=10a = 10
  4. 4.
    Subtract 2: b5=5\dfrac{b}{5} = 5; Multiply by 5: b=25b = 25
    最终答案： b=25b = 25
  5. 5.
    Subtract 2c2c: 4c+4=−124c + 4 = -12; Subtract 4: 4c=−164c = -16; Divide by 4: c=−4c = -4
    最终答案： c=−4c = -4
  6. 6.
    Let nn be the number. n+9=24n + 9 = 24; Subtract 9: n=15n = 15
    最终答案： The number is 15.

参考答案（续）

  1. 7.
    Let nn be the number. 2n+5=192n + 5 = 19; Subtract 5: 2n=142n = 14; Divide by 2: n=7n = 7
    最终答案： The number is 7.
  2. 8.
    Let nn be the number. 3n−4=113n - 4 = 11; Add 4: 3n=153n = 15; Divide by 3: n=5n = 5
    最终答案： The number is 5.
  3. 9.
    Let ww be the width. Then length =w+3= w + 3. Perimeter: 2w+2(w+3)=302w + 2(w + 3) = 30; Simplify: 4w+6=304w + 6 = 30; Subtract 6: 4w=244w = 24; Divide by 4: w=6w = 6; Length: 6+3=96 + 3 = 9
    最终答案： Width = 6 inches, Length = 9 inches.
  4. 10.
    Let aa be number of adults, cc be number of children. a+c=12a + c = 12; 8a+5c=788a + 5c = 78; From first: c=12−ac = 12 - a; Substitute: 8a+5(12−a)=788a + 5(12 - a) = 78; 3a+60=783a + 60 = 78; Subtract 60: 3a=183a = 18; Divide by 3: a=6a = 6; Then c=12−6=6c = 12 - 6 = 6
    最终答案： 6 adults and 6 children.
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需要避免的常见错误

  • 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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