Here is the article about the algebra Solved Problems for class 7. It would be better for you to read the previous topic, Algebra for Class 7, on our site. Its advantage will be that it will be easier for you to understand its theory, and without explanation, no student will be able to solve the problems. Today, algebra Solved Problems for class 7 are being presented for class 7 students.
Every topic-related problem will be solved step by step.
Simplify Algebraic Expressions for Algebra Solved Problems for Class 7
Algebraic Expressions related problems are as follows. In these problems, we will combine like terms, and then we will apply the operations given in the problem on them then we will get the answer.
Problem 1
Simplify: 3x+4x−2.
Solve:
Add the like terms 3x+4x=7x.
Don’t forget the −2-2−2.
Answer: 7x−2.
Problem 2
Simplify: 7a−4a+9−3.
Solve:
Group the letters: 7a−4a=3a.
Numbers? 9−3=6.
Answer: 3a+6.
Problem 3
Simplify: 5(2y−3).
Solve:
Distribute: 10y−15.
Answer: 10y−15.
Problem 4
Simplify: 2(3m+4)−5m.
Solve:
Expand → 6m+8.
Subtract 5m.
6m+8-5m
Answer: m+8.
Problem 5
Simplify: 4p−2(p+7).
Solve:
Expand: 4p−2p−14.
Simplify → 2p−14.
Answer: 2p−14.
Problem 6
Simplify: 3(k+2)+2(k+5).
Solve:
Expand: 3k+6+2k+10
=5k+16
Answer: 5k+4.
Problem 7
Simplify: −2(4x−1)+3x.
Solve:
Expand: −8x+2+3x
=−5x+2
Answer: −5x+2.
Problem 8
Expand & simplify: (a+3)+2(a−5).
Solve:
Work it out: a+3+2a−10
=3a−7
Answer: 3a−7.
Substitution Problems (Evaluate Expressions) in Algebra Solved Problems for class 7
Here’s where you plug numbers into letters. Kind of like testing if a code works.
Problem 1
If x=4, find 3x−5.
Solve:
3(4)−5=12−5=7
Answer: 7.
Problem 2
If a=−1, find 2a2−3a.
Solve:
Square first: (−1)2=1
Multiply: 2(1)=2.
Then −3(−1)=+3.
Add → 2+3.
Answer: 5.
Problem 3
If m=5, find (m+2)(m−1).
Solve:
=(5+2)(5-1)
=(7)(4)
=28
Answer: 28.
Problem 4
If p=−3, find p2−4p+2.
Solve:
=(-3)2-4(-3)+2
=9+12+2
=23
Answer: 22.
Problem 5
If x=2,y=3, find 2x+3y.
Solve:
=2(2)+3(3)
=4+9=13
Answer: 13.
One-Step Equations in Algebra Solved Problems for class 7
Linear algebraic equations need only one step. Just one move to free the variable.
Problem 1
x+7=19.
Solve:
Subtract 7 → x=12.
Answer: 12.
Problem 2
y−9=4.
Solve:
Add 9 → y=13.
Answer: 13.
Problem 3
5z=40.
Solve:
Divide by 5 → z=8.
Answer: 8.
Problem 4
m/16=3.
Solve:
Multiply by 16 → m=48
Answer: 48.
Problem 5
a−(−5)=12.
Solve:
Rewrite as a+5=12
Subtract 5 → a=7
Answer: 7.
Problem 6
−3x=24.
Solve:
Divide by 3→ x=−8
Answer: -8.
Two-Step and Multi-Step Equations in Algebra Solved Problems for class 7
Now it’s like peeling an onion—more than one layer.
Problem 1
2x+5=17.
Solve:
Subtract 5 → 2x=12
Divide by 2 → x=6
Answer: 6.
Problem 2
3y−4=2.
Solve:
Add 4 → 3y=6
Divide 3 → y=2
Answer: 2.
Problem 3
p/4+7=10.
Solve:
Subtract 7 → p/4+7-7=3.
Multiply 4 → p=12.
Answer: 12.
Problem 4
5m−2m=12.
Solve:
Combine → 3m=12
Divide → m=4
Answer: 4.
Problem 5
4(a−3)=20.
Solve:
Divide by 4 → a−3=5a
Add 3 → a=8
Answer: 8.
Problem 6
7(k+2)−3=25.
Solve:
Expand: 7k+14−3=25
Simplify: 7k+11=25
Subtract 11: 7k+11-11=25-11
=7k=14
Divide 7 → k=2
Answer: 2.
Problem 7
2(x−4)+3=9.
Solve:
Expand: 2x−8+3=9
Simplify: 2x−5=9
Add 5: 2x=14
Divide 2 → x=7
Answer: 7.
Fractions and Decimals in Algebra Solved Problems for class 7
Sometimes students think that fractions are scarier, but they are not. Let’s break them calmly.
Problem 1
x/3+2=11.
Solve:
Subtract 2 → x/3=11-2
x/3=9
Multiply 3→ x=27
Answer: 27.
Problem 2
(y−1)/5=2.
Solve:
Multiply 5 → y−1=10
Add 1 → y=11
Answer: 11.
Problem 3
0.4z+1.2=3.6.
Solve:
Subtract 1.2 → 0.4z=2.4
Divide 0.4 → z=6.
Answer: 6.
Problem 4
1.5m−0.9=2.1.
Solve:
Add 0.9 → 1.5m=3.0
Divide 1.5 → m=2
Answer: 2.
Problem 5
(3a+2)4=5.
Solve:
Multiply 4 → 3a+2=20.
.Subtract 2 → 3a=18
Divide 3 → a=6
Answer: 6.
Exponents and Order of Operations for Algebra Solved Problems for class 7
Remember PEMDAS/BODMAS? Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Problem 1
23+5(2).
Solve:
8+10=18
Answer: 18.
Problem 2
3^2+4^2.
Solve:
9+16=25
Answer: 25.
Problem 3
6^2-3(6).
Solve:
36−18=18
Answer: 18.
Problem 4
(3^2+1)2.
Solve:
Inside first: 9+1=10
Multiply: 20.
Answer: 20.
Problem 5
(5-2)^3.
Solve:
That’s 3^3
Answer: 27.
Polynomials (Add, Subtract, Multiply) for Algebra Solved Problems for class 7
Now, Polynomials look a bit bigger, but the rules stay the same.
Problem 1
(3x+4)+(2x−5).
Solve:
Combine → 5x−1.
Answer: 5x−1.
Problem 2
(7y−2)−(3y+6).
Solve:
Simplify → 4y−8.
Answer: 4y−8.
Problem 3
x(2x+5).
Solve:
Expand → 2x^2+5x.
Answer: 2x^2+5x.
Problem 4
(a+3)(a+2).
Solve:
FOIL it: a2+5a+6.
Answer: a2+5a+6.
Problem 5
(m−4)(m+1).
Solve:
Expand: m2+m−4m−4.
Simplify → m^2−3m−4.
Answer: m^2−3m−4..
Simple Factoring in Algebra Solved Problems for class 7
Time to pull out common factors.
Problem 1
6x+9.
Solve:
Factor out 3 → 3(2x+3).
Answer: 3(2x+3).
Problem 2
8y−12.
Solve:
Factor 4 → 4(2y−3).
Answer: 4(2y−3).
Problem 3
10a+5b.
Solve:
Factor 5 → 5(2a+b).
Answer: 5(2a+b).
Problem 4
12m−18n.
Solve:
Factor 6 → 6(2m−3n).
Answer: 6(2m−3n).
Mixed Practice for algebra Solved Problems for class 7 (A Bit of Everything)
A quick workout with different flavors of algebra.
Problem 1
Solve: 3(x+1)=2x+9.
Solve:
Expand left: 3x+3=2x+9.
Subtract 2x: x+3=9.
Subtract 3 → x=6.
Answer: 6.
Problem 2
Simplify: 5(2p−1)−3(p+4).
Solve:
Expand: 10p−5−3p−12=7p−17.
Answer: 7p−17.
Problem 3
Evaluate at x=−1: x2+3x+2.
Solve:
Substitute: 1−3+2=0.
Answer: 0.
Problem 4
Solve: 2k−3/3=5.
Solve:
Multiply 3: 2k−3=15.
Add 3: 2k=18.
Divide 2: k=9.
Answer: 9.
Problem 5
Multiply: (x+4)(x−4).
Solve:
Difference of squares → x2−16.
Answer: x2−16.
Conclusion on Algebra Solved Problems for class 7
One thing I really want you to remember: mistakes are normal. In fact, they’re a good sign—you’re actually doing the work. No one gets equations perfect the first time, and that’s fine. Just circle back, try again, and each time it’ll click a little faster.
Another thing? Don’t treat algebra like something separate from real life. It sneaks in everywhere. Sharing snacks equally with friends, working out discounts when shopping, even figuring out time management—it’s all hidden algebra. That’s why these problems matter. They sharpen the way you think, not just the way you calculate.
So keep practicing. Do a few problems daily instead of cramming a ton in one go. Build the habit. Before long, you won’t just pass algebra—you’ll feel confident with it. And hey, who knows? You might even start to enjoy it.
FAQs on Algebra Solved Problems for class 7
Q1. Why is algebra taught so early, like in class 7?
Because it’s the base for every student. Without algebra, higher math would feel impossible.
Q2. I always forget steps. Any tip?
Write. Every. Step. Even if it feels too simple. When you skip, that’s where errors sneak in. Later, once you’re confident, you can shorten.
Q3. What if I totally blank out on a problem?
If your concept of algebra is clear. Then, take a break, again focus on the problem, and remind methods of solving. Then try to solve.
Q4. How many problems should I practice daily?
No fixed rule. But honestly, 3–5 carefully solved problems each day beats solving 20 in one sitting and forgetting them by tomorrow.
Q5. Are word problems really worth the effort?
Yes, because life is basically a word problem. Money, time, distance, sharing, all of it. They train you to connect numbers with reality.
Q6. What if I don’t like math at all? Can I still get good?
Absolutely. A person does many things in his life if he is not interested in that and just focuses on consistency, then why can’t you?
Q7. Do I need to memorize formulas?
Some, yes. But don’t force it. If you understand why a formula works, it sticks naturally. Memorization becomes way easier when it makes sense.
