Hey there, genius kids! Ready to test your maths skills and prove your knowledge in algebraic expressions and equations? Don't worry, this is not a 'take-away' but a 'plus' addition to your learning side. Get your pencils, papers and thinking caps ready. It's time to solve some algebraic puzzles.

1.

What is the solution to the equation 3x + 2 = 2x + 5?

1

2

3

4

Re-arranging the equation gives x = 5 - 2, that is, 3. So, the solution to the equation is 3.

2.

If a = 6, b = 5 and c = 3. What is the value of the expression 2a + 3b - c?

10

17

27

24

Substitute a = 6, b = 5, c = 3 in 2a + 3b - c. It becomes (2 x 6) + (3 x 5) - 3, = 12 + 15 - 3 = 24.

3.

Solve for y: y ÷ 3 + 4 = 7

6

7

8

9

First subtract 4 from both sides, getting y รท 3 = 7 - 4. Then, multiply both sides by 3 to get y = 9.

4.

What is the expression for the statement: 'Three times a number n, increased by four'?

n + 3 + 4

n + 12

3n - 4

3n + 4

'Three times a number n' is 3n, and 'increased by four' translates into the operation +4. So, the expression is 3n + 4.

5.

Solve ^{1}⁄_{2}a + 2 = 5.

4

6

8

10

Subtract 2 from both sides, getting ^{1}⁄_{2}a = 3. Multiply both sides by 2 to solve for a, so a = 6

6.

Solve for y: 10y + 5 = 25.

2

3

6

8

Subtract 5 from both sides. It gives you 10y = 20. Dividing both sides by 10, we get y = 2.

7.

Expand the expression: 4(2x + 3)

8x + 12

6x + 7

8x + 9

10x + 12

By the distributive law, 4(2x + 3) becomes (4 x 2x) + (4 x 3), which is 8x + 12.

8.

Find the value of 3x - 4 when x = 2.

1

2

6

10

Substitute 'x' with '2' in 3x - 4. Therefore, (3 x 2) - 4 = 6 - 4, which is 2.

9.

What will be the result when y = 3 is substituted into the equation 2y^{2} - 4 =?

14

16

18

20

Substitute 'y' with '3' in the equation. Therefore, 2 x (3^{2}) - 4, which is 2 x 9 - 4, which results in 18 - 4, and it's 14.

10.

Simplify the expression: 2(5x - 3) + 4

10x + 2

10x - 6

10x - 2

10x - 6 + 4

Expand using the distributive property to get 10x - 6 + 4, then combine like terms to get 10x - 2.