شرح إعادة ترتيب الصيغ المركبة

Worked example

1. 1

   $y=2t^3+5k$ — Make t the subject. t was cubed, then doubled, then 5k was added. We undo those in reverse.

2. 2

   $y-5k=2t^3$ — Take 5k from both sides. The +5k was done last, so it is undone first.

3. 3

   $\frac{y-5k}{2}=t^3$ — Divide both sides by 2. The 2 divides the whole side, so y − 5k goes on top.

4. 4

   $t=\sqrt[3]{\frac{y-5k}{2}}$ — Cube root both sides. The root covers the whole side, not just the y.

Worked example

1. 1

   $A=k(r^2+h^2)$ — Make r the subject. r was squared, then $h^2$ was added, then the bracket was multiplied by k.

2. 2

   $\frac{A}{k}=r^2+h^2$ — Divide both sides by k. The k multiplies the bracket, and it was done last.

3. 3

   $\frac{A}{k}-h^2=r^2$ — Take $h^2$ from both sides so $r^2$ is on its own.

4. 4

   $r=\pm \sqrt{\frac{A}{k}-h^2}$ — Square root both sides. It covers both terms. Keep ± unless r is a length, which cannot be negative.

Worked example

1. 1

   $k=\sqrt{\frac{3b+m}{b+4}}$ — Make b the subject. b is in two places, inside a fraction, inside a square root.

2. 2

   $k^2=\frac{3b+m}{b+4}$ — Square both sides. The root was done last, so it comes off first.

3. 3

   $k^2(b+4)=3b+m$ — Multiply both sides by the bottom, $b+4$. Now there is no fraction.

4. 4

   $k^{2}b+4k^2=3b+m$ — Expand the bracket: $k^2\times b$ and $k^2\times 4$. The b terms are marked.

5. 5

   $k^{2}b-3b=m-4k^2$ — Take 3b from both sides and take $4k^2$ from both sides. All the b terms are now on the left.

6. 6

   $b(k^2-3)=m-4k^2$ — Factorise: both terms on the left have b, so take b out. Now b appears once.

7. 7

   $b=\frac{m-4k^2}{k^2-3}$ — Divide both sides by $k^2-3$ to leave b on its own.

Worked example

1. 1

   $w=\frac{3(t-2)}{t+4}$ — Make t the subject. t is on the top and the bottom.

2. 2

   $w(t+4)=3(t-2)$ — Multiply both sides by the bottom, $t+4$, to clear the fraction.

3. 3

   $wt+4w=3t-6$ — Expand both brackets: $3\times (-2)=-6$. The t terms are marked.

4. 4

   $wt-3t=-6-4w$ — Take 3t from both sides and 4w from both sides. The −6 stays on the right with its minus.

5. 5

   $t(w-3)=-6-4w$ — Factorise: take t out of the left side, so t appears once.

6. 6

   $t=\frac{-6-4w}{w-3}$ — Divide both sides by $w-3$. This answer is correct.