**GSEB Solutions for Class 7 Mathematics – Brackets (English Medium)**

GSEB SolutionsMathsScience

**Exercise**

**Solution 1(1):**

[3 + 2{3 × (6 ÷ 2 )}] – 1

= [3 + 2{3 × 3}] – 1

= [3 + 2{9}] – 1

= [3 + 18] – 1

= [21] – 1

= 21 – 1

= 20

**Solution 1(2):**

[6 + 2{2 × (10 ÷ 2)}] – 4

= [6 + 2{2 × 5}] – 4

= [6 + 2{10}] – 4

= [6 + 20] – 4

= [26] – 4

= 26 – 4

= 22

**Solution 1(3):**

[3 + 2{2 × (6 ÷ 2)}] – 3

= [3 + 2{2 × 3}] – 3

= [3 + 2{6}] – 3

= [3 + 12] – 3

= [15] – 3

= 15 – 3

= 12

**Solution 1(4):**

[4 + 3{4 × (6 ÷ 3)}] – 1

= [4 + 3{4 × 2}] – 1

= [4 + 3{8}] – 1

= [4 + 24] – 1

= [28] – 1

= 28 – 1

= 27

**Solution 1(5):**

[3 + 2{3 × (6 ÷ 2)}] – 2

= [3 + 2{3 × 3}] – 2

= [3 + 2{9}] – 2

= [3 + 18] – 2

= [21] – 2

= 21 – 2

= 19

**Solution 1(6):**

[4 + 5{2 × (5 – 1)}] – 4

= [4 + 5{2 × 4}] – 4

= [4 + 5{8}] – 4

= [4 + 40] – 4

= [44] – 4

= 44 – 4

= 40

**Solution 1(7):**

[3 + 4{2 × (3 – 1)}] + 7

= [3 + 4{2 × 2}] + 7

= [3 + 4 × {4}] + 7

= [3 + 16] + 7

= [19] + 7

= 19 + 7

= 26

**Solution 1(8):**

[1 + 2{3 × (4 – 3)}] × 2

= [1 + 2{3 × (1)}] × 2

= [1 + 2{3}] × 2

= [1 + 6] × 2

= [7] × 2

= 7 × 2

= 14

**Solution 2(1):**

a – [a + {a – (a + 2)} + 2]

= a – [a + {a – a – 2)} + 2]

= a – [a + {- 2)} + 2]

= a – [a – 2 + 2]

= a – [a]

= a – a

= 0

**Solution 2(2):**

3y – [2y – {4 – (y – 2)} – 5]

= 3y – [2y – {4 – y + 2} – 5]

= 3y – [2y – {6 – y} – 5]

= 3y – [2y – 6 + y – 5]

= 3y – [2y + y – 6 – 5]

= 3y – [3y – 11]

= 3y – 3y + 11

= 11

**Solution 2(3):**

3a – [{3a – (y – 2y)} – 3a] + y

= 3a – [{3a – (-y)} – 3a] + y

= 3a – [{3a + y} – 3a] + y

= 3a – [3a + y – 3a] + y

= 3a – [y] + y

= 3a – y + y

= 3a

**Solution 2(4):**

[3x^{2} – {4x – (2x^{2} + 5x – 3)}] – 5

= [3x^{2} – {4x – 2x^{2} – 5x + 3}] – 5

= [3x^{2} – 4x + 2x^{2} + 5x – 3] – 5

= [3x^{2} + 2x^{2} – 4x + 5x – 3] – 5

= [5x^{2} + x – 3] – 5

= 5x^{2} + x – 3 – 5

= 5x^{2} + x – 8

**Solution 2(5):**

-x – [x – {-(- x)}]

= -x – [x – {x)}]

= -x – [x – x]

= – x – 0

= (- x)

**Solution 3(1):**

[6 + 3{4 × (9 – 2)}] + 10

Verification:

[6 + 3{4 × (9 – 2)}] + 10

= [6 + 3{4 × 7}] + 10

= [6 + 3{28}] + 10

= [6 + 84] + 10

= [90] + 10

= 90 + 10

= 100

**Solution 3(2):**

2[6 + 3{4 × (5 – 1)}] – 8

Verification:

2[6 + 3{4 × (5 – 1)}] – 8

= 2[6 + 3{4 × (4)}] – 8

= 2[6 + 3{16}] – 8

= 2[6 + 48] – 8

= 2[54] – 8

= 108 – 8

= 100

**Solution 3(3):**

2[9{5 × (7 – 4)} ÷ 3] + 10

Verification:

2 [9{5 × (7 – 4)} ÷ 3] + 10

= 2[9{5 × (3)} ÷ 3] + 10

= 2[9{15} ÷ 3] + 10

= 2[135 ÷ 3] + 10

= 2[45] + 10

= 90 + 10

= 100

**Solution 3(4):**

[4{8 × (9 ÷ 3)} + 5] – 1

Verification:

[4{8 × (9 ÷ 3)} + 5] – 1

= [4{8 × (3)} + 5] – 1

= [4{24} + 5] – 1

= [96 + 5] – 1

= [101] – 1

= 101 – 1

= 100

**Solution 3(5):**

[3{7 × (10 ÷ 2)} – 6] + 1

Verification:

[3{7 × (10 ÷ 2)} – 6] + 1

= [3{7 × (5)} – 6] + 1

= [3{35} – 6] + 1

= [105 – 6] + 1

= [99] + 1

= 99 + 1

= 100

**Practice – 1**

**Solution 1:**

7 + {3 + (5 – 3)}

= 7 + {3 + 2}

= 7 + {5}

= 7 + 5

= 12

**Solution 2:**

10 – {8 + (4 ÷ 2)}

= 10 – {8 + 2}

= 10 – 10

= 0

**Solution 3:**

19 – [30 – {12 + (8 – 3)}]

= 19 – [30 – {12 + 5}]

= 19 – [30 – 17]

= 19 – 13

= 6

**Solution 4:**

5x – [-{-(-5x)}]

= 5x – [-{5x}]

= 5x + 5x

= 10x

**Solution 5:**

30 – [{17 + (9 – 4)} + 17]

= 30 – [{17 + 5} + 17]

= 30 – [{22} + 17]

= 30 – [39]

= (-9)

**Solution 6:**

5 + [18 – {27 – (12 – 3)}] – 6

= 5 + [18 – {27 – (9)}] – 6

= 5 + [18 – {18}] – 6

= 5 + [0] – 6

= 5 – 6

= (-1)

**Solution 7:**

{(3x^{2} – 6x + 5) + (2x – 2x^{2} + 5)} – (x^{2} – 4x +10)

= {3x^{2} – 6x + 5 + 2x – 2x^{2} + 5} – (x^{2} – 4x +10)

= {3x^{2} – 2x^{2} – 6x + 2x + 5 + 5} – (x^{2} – 4x +10)

= {x^{2} – 4x + 10} – (x^{2} – 4x + 10)

= x^{2} – 4x + 10 – x^{2} + 4x – 10)

= x^{2} – x^{2} – 4x + 4x + 10 – 10

= 0

**Solution 8:**

3m – {m + 2(5 – m)}

= 3m – {m + 10 – 2m}

= 3m – {-m + 10}

= 3m + m – 10

= 4m – 10

**Solution 9:**

[{5x – (x + 3y)} – {x + (2x – y)}]

= [{5x – x – 3y} – {x + 2x – y}]

= [{4x – 3y} – {3x – y}]

= [4x – 3y – 3x + y]

= 4x – 3x – 3y + y

= x – 2y

**Solution 10:**

15 – [3x – {x + (2x + 5) – (x + 3)}]

= 15 – [3x – {x + 2x + 5 – x – 3}]

= 15 – [3x – {x + 2x – x + 5 – 3}]

= 15 – [3x – {2x + 2}]

= 15 – [3x – 2x – 2]

= 15 – [x – 2]

= 15 – x + 2

= 17 – x