Linear equations

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शिक्षकों के लिए: Linear equations (Mathematics, Algebra) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।

लेसन नोट्स स्लाइड्स प्रैक्टिस सवाल

लेसन नोट्स

What a linear equation is

A linear equation contains an unknown (such as x) to the power 1 only, with no x² or \frac{1}{x} terms.
To solve it means to find the value of the unknown that makes both sides equal.
Keep the equation balanced: whatever you do to one side you must do to the other.

Solving one- and two-step equations

Use inverse operations to undo what has been done to x: the inverse of + is −, of × is ÷.
Example: 3x + 5 = 20. Subtract 5: 3x = 15. Divide by 3: x = 5.
Check by substituting back into the original equation.

Unknowns on both sides and brackets

Expand any brackets first: 2(x + 3) = 2x + 6.
Collect the x terms on one side, then the numbers on the other. Move the smaller x term to avoid negative coefficients.
Example: 5x - 4 = 2x + 11 gives 3x = 15, so x = 5.

Equations with fractions

Multiply every term by the common denominator to clear the fractions.
Example: \frac{x}{4} + 2 = 5 gives \frac{x}{4} = 3, so x = 12.
For \frac{x+1}{3} = \frac{x-2}{2}, multiply both sides by 6: 2(x+1) = 3(x-2).

Common errors

Changing a sign wrongly when moving a term across the equals sign.
Dividing only one term instead of the whole side.
Forgetting to multiply every term when clearing fractions, or not expanding a bracket fully (-2(x-3) = -2x + 6, not -2x - 6).

स्लाइड्स

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 33 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.What does it mean to solve an equation?
Easy
- ARewrite it in a different order
- BFind the value of the unknown that makes both sides equal
- CExpand all the brackets
- DDraw its graph
2.Solve x + 9 = 15.
Easy
- Ax = 6
- Bx = 24
- Cx = -6
- Dx = 135
3.Solve 4x = 28.
Easy
- Ax = 24
- Bx = 7
- Cx = 32
- Dx = 112
4.Solve x - 8 = 3.
Easy
- Ax = -5
- Bx = 5
- Cx = 11
- Dx = 24
5.Solve 2x + 7 = 19.
Easy
- Ax = 6
- Bx = 13
- Cx = 5
- Dx = 26
6.Solve 5x - 2 = 18.
Easy
- Ax = 3.2
- Bx = 4
- Cx = 16
- Dx = 90
7.Solve 3x + 4 = 1.
Easy
- Ax = 1
- Bx = -1
- Cx = \frac{5}{3}
- Dx = -\frac{5}{3}
8.Solve \frac{x}{3} + 1 = 6.
Easy
- Ax = 7
- Bx = 15
- Cx = 21
- Dx = 5

और सवाल

9.Solve 6 - x = 2.
Easy
- Ax = -4
- Bx = 8
- Cx = 4
- Dx = -8
10.Solve 6x - 5 = 2x + 11.
Medium
- Ax = 1.5
- Bx = 4
- Cx = 6
- Dx = 16
11.Solve 3(x + 2) = 21.
Medium
- Ax = 5
- Bx = 7
- Cx = 3
- Dx = 19
12.Solve 2(3x - 1) = 22.
Medium
- Ax = 4
- Bx = 3.67
- Cx = 12
- Dx = 2
13.Solve 8 - 3x = 2.
Medium
- Ax = -2
- Bx = 2
- Cx = \frac{10}{3}
- Dx = 6
14.Solve 4x + 3 = 7x - 9.
Medium
- Ax = 4
- Bx = -4
- Cx = 2
- Dx = 12
15.Solve 5(x - 2) = 3(x + 4).
Medium
- Ax = 11
- Bx = 1
- Cx = 6
- Dx = 7
16.Solve \frac{x + 1}{3} = 4.
Medium
- Ax = 11
- Bx = 12
- Cx = 13
- Dx = 3
17.Solve \frac{2x}{5} = 6.
Medium
- Ax = 2.4
- Bx = 12
- Cx = 15
- Dx = 30
18.Solve \frac{x}{2} + \frac{x}{3} = 10.
Medium
- Ax = 12
- Bx = 6
- Cx = 50
- Dx = 5
19.Solve \frac{x + 1}{3} = \frac{x - 2}{2}.
Medium
- Ax = 8
- Bx = 4
- Cx = 1
- Dx = 7
20.Expanding -2(x - 3) gives:
Medium
- A-2x - 6
- B-2x + 6
- C2x - 6
- D-2x + 3
21.A number is multiplied by 3 and then 4 is added to give 22. What is the number?
Easy
- A6
- B8
- C26
- D5.5
22.The perimeter of a rectangle is 30 cm. Its length is x + 5 and its width is x. What is x?
Medium
- A5
- B10
- C7.5
- D2.5
23.Three consecutive integers add up to 72. What is the smallest?
Medium
- A23
- B24
- C25
- D22
24.Why must you do the same operation to both sides of an equation?
Easy
- ATo make the numbers smaller
- BTo keep the equation balanced
- CTo remove the unknown
- DSo that the answer is positive
25.In 5x - 4 = 2x + 11, what is the best first step?
Medium
- ASubtract 2x from both sides
- BDivide by 5
- CAdd x to both sides
- DSubtract 11 from the left only
26.The equation x² = 9 is a linear equation.
Easy
True or false?
27.The solution of x + 4 = 10 is x = 6.
Easy
True or false?
28.You can check a solution by substituting it back into the original equation.
Easy
True or false?
29.If 3x = 12, then x = 36.
Easy
True or false?
30.2(x + 3) = 2x + 3.
Medium
True or false?
31.Which of these equations have the solution x = 3?
Medium
- A2x + 1 = 7
- Bx - 1 = 4
- C5x = 15
- Dx + 6 = 8
- E4x - 2 = 10
32.Which two inverse operations, in this order, solve x/4 + 2 = 5 by undoing the operations applied to x? Select both.
Medium
- ASubtract 2 from both sides
- BMultiply both sides by 4
- CAdd 2 to both sides
- DDivide both sides by 4
33.Solve 4(x - 1) = 2x + 8, showing each step.
Medium

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