A5a - Rearranging formulas to change the subject - BossMaths.com - Free Printable

Let’s solve each problem one by one. We want to make x the subject — that means we want x alone on one side of the equation.

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1) 0.2x = 9y

We need to get x by itself. Right now, x is multiplied by 0.2. So we divide both sides by 0.2:

→ x = 9y ÷ 0.2

Dividing by 0.2 is the same as multiplying by 5 (because 1 ÷ 0.2 = 5):

→ x = 45y

✔ Final answer for #1: x = 45y

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2) mx = 6k

x is multiplied by m. To isolate x, divide both sides by m:

→ x = 6k ÷ m

✔ Final answer for #2: x = 6k/m

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3) 3x = √v

x is multiplied by 3. Divide both sides by 3:

→ x = √v 3

Or written neatly: x = √v / 3

✔ Final answer for #3: x = √v / 3

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4) (3p)/q = x/4

We want x alone. Right now, x is divided by 4. Multiply both sides by 4:

→ 4 × (3p/q) = x

Multiply 4 and 3p: 12p

→ x = 12p / q

✔ Final answer for #4: x = 12p/q

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5) 81y = x² (assume x > 0)

x is squared. To undo squaring, take square root of both sides.

→ √(81y) = √(x²)

√(x²) = x (since x > 0, we don’t need ±)

√(81y) = √81 × √y = 9√y

→ x = 9√y

✔ Final answer for #5: x = 9√y

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6) 3x² = 40t (assume x > 0)

First, divide both sides by 3 to get x² alone:

→ x² = 40t / 3

Now take square root of both sides:

→ x = √(40t / 3)

We can simplify √(40t/3). Let’s break it down:

√(40t/3) = √(40t) / √3 = (√4 × √10 × √t) / √3 = (2√(10t)) / √3

But usually, we rationalize or leave as is unless told otherwise. Since no simplification instruction, we can write:

→ x = √(40t/3)

Alternatively, factor inside:

40t/3 = (4×10t)/3 → so √(4×10t/3) = 2√(10t/3)

That’s simpler!

→ x = 2√(10t/3)

✔ Final answer for #6: x = 2√(10t/3)

*(Note: Some might prefer to write it as √(40t/3), but 2√(10t/3) is more simplified.)*

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7) x³ = 10w

x is cubed. To undo cube, take cube root of both sides:

→ x = ∛(10w)

✔ Final answer for #7: x = ∛(10w)

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8) [4(r + 4)] / 3 = u x⁵

We want x alone. First, let’s get rid of the fraction and the u.

Step 1: Multiply both sides by 3 to eliminate denominator:

→ 4(r + 4) = 3u x⁵

Step 2: Divide both sides by 3u to isolate x⁵:

→ x⁵ = [4(r + 4)] / (3u)

Step 3: Take fifth root of both sides:

→ x = ⁿ√[4(r + 4)/(3u)] where n=5

So:

→ x = ∛? No — fifth root!

→ x = \sqrt[5]{ \frac{4(r + 4)}{3u} }

✔ Final answer for #8: x = \sqrt[5]{ \frac{4(r + 4)}{3u} }

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## ✔ FINAL ANSWERS:

1) x = 45y
2) x = 6k/m
3) x = √v / 3
4) x = 12p/q
5) x = 9√y
6) x = 2√(10t/3)
7) x = ∛(10w)
8) x = \sqrt[5]{ \frac{4(r + 4)}{3u} }