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# Practice - Algebra Expressions and Equations - 04

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 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.
2.
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.
3.
Solve for y: y ÷ 3 + 4 = 7
6
7
8
9
First subtract 4 from both sides, getting y ÷ 3 = 7 - 4. Then, multiply both sides by 3 to get y = 9.
4.
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.
5.
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.
6.
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.
7.
What will be the result when y = 3 is substituted into the equation 2y2 - 4 =?
14
16
18
20
Substitute 'y' with '3' in the equation. Therefore, 2 x (32) - 4, which is 2 x 9 - 4, which results in 18 - 4, and it's 14.
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.
Solve 12a + 2 = 5.
4
6
8
10
Subtract 2 from both sides, getting 12a = 3. Multiply both sides by 2 to solve for a, so a = 6
10.
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.
Author:  Graeme Haw
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