Algebra Practice Questions
with Detailed Solutions
(100 Questions – From Basic to Advanced)
Basic (30) Algebra Questions and
Solutions
Section 1: Simplification & Basic Operations
Q1. Simplify:
(3x+5)+(2x−7)(3x + 5) + (2x - 7)(3x+5)+(2x−7)
Solution:
Combine like terms:
3x+2x+5−7=5x−23x + 2x + 5 - 7 = 5x -
23x+2x+5−7=5x−2
Answer: 5x - 2
Q2. Simplify:
(4a−6)−(2a+3)(4a - 6) - (2a + 3)(4a−6)−(2a+3)
Solution:
Distribute the minus:
4a−6−2a−3=(4a−2a)+(−6−3)=2a−94a - 6 - 2a - 3 = (4a
- 2a) + (-6 - 3) = 2a - 94a−6−2a−3=(4a−2a)+
(−6−3)=2a−9
Answer: 2a - 9
Q3. Simplify:
(5x)(2x+3)(5x)(2x + 3)(5x)(2x+3)
,Solution:
Multiply each term:
5x⋅2x+5x⋅3=10x2+15x5x \cdot 2x + 5x \cdot 3 = 10x^2
+ 15x5x⋅2x+5x⋅3=10x2+15x
Answer: 10x² + 15x
Q4. Simplify:
(x+4)(x−2)(x + 4)(x - 2)(x+4)(x−2)
Solution:
Use distributive property (FOIL):
x2−2x+4x−8=x2+2x−8x^2 - 2x + 4x - 8 = x^2 + 2x -
8x2−2x+4x−8=x2+2x−8
Answer: x² + 2x - 8
Q5. Expand and simplify:
(2x+3)2(2x + 3)^2(2x+3)2
Solution:
Square formula: (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab +
b^2(a+b)2=a2+2ab+b2
(2x)2+2(2x)(3)+(3)2=4x2+12x+9(2x)^2 + 2(2x)(3) +
(3)^2 = 4x^2 + 12x + 9(2x)2+2(2x)(3)+(3)2=4x2+12x+9
Answer: 4x² + 12x + 9
Section 2: Solving Linear Equations
Q6. Solve for xxx:
2x+5=152x + 5 = 152x+5=15
Solution:
Subtract 5:
, 2x=102x = 102x=10
Divide by 2:
x=5x = 5x=5
Answer: x = 5
Q7. Solve:
3x−7=113x - 7 = 113x−7=11
Solution:
Add 7:
3x=183x = 183x=18
Divide by 3:
x=6x = 6x=6
Answer: x = 6
Q8. Solve:
5x+2=3x+105x + 2 = 3x + 105x+2=3x+10
Solution:
Bring terms together:
5x−3x=10−25x - 3x = 10 - 25x−3x=10−2 2x=8 ⟹
x=42x = 8 \implies x = 42x=8⟹x=4
Answer: x = 4
Q9. Solve:
4(x−2)=124(x - 2) = 124(x−2)=12
with Detailed Solutions
(100 Questions – From Basic to Advanced)
Basic (30) Algebra Questions and
Solutions
Section 1: Simplification & Basic Operations
Q1. Simplify:
(3x+5)+(2x−7)(3x + 5) + (2x - 7)(3x+5)+(2x−7)
Solution:
Combine like terms:
3x+2x+5−7=5x−23x + 2x + 5 - 7 = 5x -
23x+2x+5−7=5x−2
Answer: 5x - 2
Q2. Simplify:
(4a−6)−(2a+3)(4a - 6) - (2a + 3)(4a−6)−(2a+3)
Solution:
Distribute the minus:
4a−6−2a−3=(4a−2a)+(−6−3)=2a−94a - 6 - 2a - 3 = (4a
- 2a) + (-6 - 3) = 2a - 94a−6−2a−3=(4a−2a)+
(−6−3)=2a−9
Answer: 2a - 9
Q3. Simplify:
(5x)(2x+3)(5x)(2x + 3)(5x)(2x+3)
,Solution:
Multiply each term:
5x⋅2x+5x⋅3=10x2+15x5x \cdot 2x + 5x \cdot 3 = 10x^2
+ 15x5x⋅2x+5x⋅3=10x2+15x
Answer: 10x² + 15x
Q4. Simplify:
(x+4)(x−2)(x + 4)(x - 2)(x+4)(x−2)
Solution:
Use distributive property (FOIL):
x2−2x+4x−8=x2+2x−8x^2 - 2x + 4x - 8 = x^2 + 2x -
8x2−2x+4x−8=x2+2x−8
Answer: x² + 2x - 8
Q5. Expand and simplify:
(2x+3)2(2x + 3)^2(2x+3)2
Solution:
Square formula: (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab +
b^2(a+b)2=a2+2ab+b2
(2x)2+2(2x)(3)+(3)2=4x2+12x+9(2x)^2 + 2(2x)(3) +
(3)^2 = 4x^2 + 12x + 9(2x)2+2(2x)(3)+(3)2=4x2+12x+9
Answer: 4x² + 12x + 9
Section 2: Solving Linear Equations
Q6. Solve for xxx:
2x+5=152x + 5 = 152x+5=15
Solution:
Subtract 5:
, 2x=102x = 102x=10
Divide by 2:
x=5x = 5x=5
Answer: x = 5
Q7. Solve:
3x−7=113x - 7 = 113x−7=11
Solution:
Add 7:
3x=183x = 183x=18
Divide by 3:
x=6x = 6x=6
Answer: x = 6
Q8. Solve:
5x+2=3x+105x + 2 = 3x + 105x+2=3x+10
Solution:
Bring terms together:
5x−3x=10−25x - 3x = 10 - 25x−3x=10−2 2x=8 ⟹
x=42x = 8 \implies x = 42x=8⟹x=4
Answer: x = 4
Q9. Solve:
4(x−2)=124(x - 2) = 124(x−2)=12
