CBSE Class 7 Mental Maths Simple Equations Worksheet - Free Printable

It looks like you've uploaded an image containing a list of algebraic equations and their solutions, but the actual problem or task you want me to solve isn't clearly specified. However, I can help you by:

1. Solving the given equations step-by-step, if that's what you need.
2. Verifying the provided answers, since many are already listed.

Let’s go through the first few problems in detail and verify or solve them. Then, I’ll explain how to approach such problems systematically.

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Problem (iv): *Adding 5 to one third of x gives 8.*

Step 1: Translate into an equation

> "One third of x" → $\frac{1}{3}x$
> "Adding 5 to it gives 8" → $\frac{1}{3}x + 5 = 8$

So the equation is:
$$
\frac{1}{3}x + 5 = 8
$$

Step 2: Solve for $x$

Subtract 5 from both sides:
$$
\frac{1}{3}x = 8 - 5 = 3
$$

Multiply both sides by 3:
$$
x = 3 \times 3 = 9
$$

✔ Answer: $x = 9$

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Problem (v): *Adding 7 to $\frac{3}{2}$ of a number gives 29.*

Let the number be $x$.

Then:
$$
\frac{3}{2}x + 7 = 29
$$

Subtract 7:
$$
\frac{3}{2}x = 22
$$

Multiply both sides by $\frac{2}{3}$:
$$
x = 22 \times \frac{2}{3} = \frac{44}{3}
$$

✔ Answer: $x = \frac{44}{3}$ or $14\frac{2}{3}$

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Now let's look at Question 2, which has several equations:

#### (i) $5x = 25$

Divide both sides by 5:
$$
x = \frac{25}{5} = 5
$$

✔ Answer: $x = 5$

#### (ii) $\frac{y}{4} = 20$

Multiply both sides by 4:
$$
y = 80
$$

✔ Answer: $y = 80$

#### (iii) $\frac{x}{5} = 2x - 7$

Multiply both sides by 5 to eliminate denominator:
$$
x = 5(2x - 7) = 10x - 35
$$

Bring all terms to one side:
$$
x - 10x = -35 \Rightarrow -9x = -35
\Rightarrow x = \frac{35}{9}
$$

✔ Answer: $x = \frac{35}{9}$

#### (iv) $3y - 13 = 8$

Add 13:
$$
3y = 21 \Rightarrow y = 7
$$

✔ Answer: $y = 7$

#### (v) $2(2b + 8) = 256$

Expand:
$$
4b + 16 = 256
$$

Subtract 16:
$$
4b = 240 \Rightarrow b = 60
$$

✔ Answer: $b = 60$

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Question 3: $\frac{3x + 49}{7} = 7$

Multiply both sides by 7:
$$
3x + 49 = 49
$$

Subtract 49:
$$
3x = 0 \Rightarrow x = 0
$$

But the answer listed is not given here — maybe it's missing? Or perhaps it's a typo?

Wait — in your list, #5 says $x = 4$, but that doesn’t match this equation.

Let’s check: Is $x = 4$ a solution?

Plug into left side:
$$
\frac{3(4) + 49}{7} = \frac{12 + 49}{7} = \frac{61}{7} \ne 7
$$

So no, $x = 4$ is not correct.

Correct solution is $x = 0$, as shown above.

✘ So either the equation or the answer is wrong.

Let’s suppose instead the equation was meant to be:
$$
\frac{3x + 49}{7} = 10 \quad \text{(for example)}
$$
then $3x + 49 = 70 \Rightarrow 3x = 21 \Rightarrow x = 7$

But we don’t know.

Alternatively, maybe there’s a formatting issue.

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Now checking some of the listed answers:

- #5: $x = 4$
- #6: $P = -8$
- #7: $z = -2$
- #8: $x = -1$
- #9: $y = -\frac{4}{3}$
- #10: $x = \frac{5}{6}$

These seem to be answers to other equations not shown in the image.

So it appears that:

- The top part has word problems (iv), (v)
- Then equations to solve (Q2, Q3)
- Then a list of answers numbered 4–36, possibly corresponding to problems not fully visible

But without knowing which specific problem you want solved, I can only assume you want help with solving the equations or verifying the answers.

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Let's do a summary:

| Problem | Equation | Solution |
|--------|----------|---------|
| (iv) | $\frac{1}{3}x + 5 = 8$ | $x = 9$ |
| (v) | $\frac{3}{2}x + 7 = 29$ | $x = \frac{44}{3}$ |
| 2(i) | $5x = 25$ | $x = 5$ |
| 2(ii) | $\frac{y}{4} = 20$ | $y = 80$ |
| 2(iii) | $\frac{x}{5} = 2x - 7$ | $x = \frac{35}{9}$ |
| 2(iv) | $3y - 13 = 8$ | $y = 7$ |
| 2(v) | $2(2b + 8) = 256$ | $b = 60$ |
| 3 | $\frac{3x + 49}{7} = 7$ | $x = 0$ |

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Final Notes:

- Many of the listed answers (e.g., #5: $x=4$) do not match any of the equations shown.
- Possibly, the image contains multiple questions and the answers are mixed up.
- If you can specify which problem you want solved (e.g., “solve question 2(iii)” or “verify answer #15”), I can give a precise explanation.

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✔ Conclusion:

If your goal was to solve the equations in Q2, then here are the correct solutions:

- (i) $x = 5$
- (ii) $y = 80$
- (iii) $x = \frac{35}{9}$
- (iv) $y = 7$
- (v) $b = 60$

And for the word problems:

- (iv) $x = 9$
- (v) $x = \frac{44}{3}$

Let me know if you’d like me to solve any specific numbered item from the list (like #17, #25, etc.) or if you want explanations for how to solve linear equations in general.