Linear Equations in one Variable — Flashcards
ICSE · Class 8 · Mathematics
24 flashcards for Linear Equations in one Variable (ICSE Class 8 Mathematics) to test yourself on key terms and facts.
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Solve: 21 - 3(a - 7) = a + 20
Answer
Step 1: Expand the bracket: 21 - 3a + 21 = a + 20 Step 2: Combine like terms: 42 - 3a = a + 20 Step 3: Move terms: 42 - 20 = a + 3a Step 4: 22 = 4a Step 5: a = 22/4 = 5 1/2 Answer: a = 5 1/2…
Solve: (y + 2)/4 - (y - 3)/3 = 1/2
Answer
Step 1: L.C.M. of 4, 3, and 2 is 12. Step 2: Multiply every term by 12. Step 3: 3(y + 2) - 4(y - 3) = 6 Step 4: 3y + 6 - 4y + 12 = 6 Step 5: -y + 18 = 6 Step 6: -y = -12 Step 7: y = 12 Answer: y = 12…
Solve: 5/x = 7/(x - 4)
Answer
Step 1: Cross-multiply carefully: 7x = 5(x - 4) Step 2: Expand: 7x = 5x - 20 Step 3: Move terms: 7x - 5x = -20 Step 4: 2x = -20 Step 5: x = -10 Answer: x = -10…
Solve: (a - 2)/(a + 4) = (a - 3)/(a + 1)
Answer
Step 1: Cross-multiply. Step 2: (a - 2)(a + 1) = (a - 3)(a + 4) Step 3: Expand both sides. Left: a^2 - a - 2 Right: a^2 + a - 12 Step 4: Cancel a^2 from both sides. Step 5: -a - 2 = a - 12 Step 6: -2a…
Solve the equation and then find y if 1/x + 1/y = 3: (2x + 1)/10 - (3 - 2x)/15 = (x - 2)/6
Answer
Step 1: L.C.M. of 10, 15, and 6 is 30. Step 2: Multiply every term by 30. Step 3: 3(2x + 1) - 2(3 - 2x) = 5(x - 2) Step 4: 6x + 3 - 6 + 4x = 5x - 10 Step 5: 10x - 3 = 5x - 10 Step 6: 5x = -7 Step 7: x…
Why does adding, subtracting, multiplying, or dividing the same non-zero number on both sides keep an equation unchanged?
Answer
Because both sides stay equal. If the same change is made to each side, the balance is not disturbed. Example: If x = 5, then x + 3 = 8 and 5 + 3 = 8. The equality is still true. This is why the same …
What is the value of the variable in a linear equation called?
Answer
The value of the variable that solves a linear equation is called its root. A linear equation has only one solution. Quick example: if 2x = 8, then x = 4, so 4 is the root.
Write consecutive numbers, consecutive even numbers, and consecutive odd numbers in algebraic form.
Answer
Consecutive numbers: x, x + 1, x + 2, ... Consecutive even numbers: x, x + 2, x + 4, ... where x is even Consecutive odd numbers: x, x + 2, x + 4, ... where x is odd Quick example: if x = 6, then the …
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