Topic:Change of subject of formula Let's Take number number 1-20

Hey Nmk, good to see you again. Here are the solutions for problems 1-8: 1) Given formula: $y = x + 8$. Make $x$ the subject. Step 1: Subtract 8 from both sides of the equation. $$y - 8 = x + 8 - 8$$ $$y - 8 = x$$ Step 2: Rewrite with $x$ on the left side. $$x = y - 8$$ The subject is $\boxed{x = y - 8}$. 2) Given formula: $y = x - 3$. Make $x$ the subject. Step 1: Add 3 to both sides of the equation. $$y + 3 = x - 3 + 3$$ $$y + 3 = x$$ Step 2: Rewrite with $x$ on the left side. $$x = y + 3$$ The subject is $\boxed{x = y + 3}$. 3) Given formula: $b = a + c$. Make $a$ and $c$ the subject. a) Make $a$ the subject: Step 1: Subtract $c$ from both sides of the equation. $$b - c = a + c - c$$ $$b - c = a$$ Step 2: Rewrite with $a$ on the left side. $$a = b - c$$ The subject is $\boxed{a = b - c}$. b) Make $c$ the subject: Step 1: Subtract $a$ from both sides of the equation. $$b - a = a + c - a$$ $$b - a = c$$ Step 2: Rewrite with $c$ on the left side. $$c = b - a$$ The subject is $\boxed{c = b - a}$. 4) Given formula: $y = 3x$. Make $x$ the subject. Step 1: Divide both sides of the equation by 3. $$\frac{y}{3} = \frac{3x}{3}$$ $$\frac{y}{3} = x$$ Step 2: Rewrite with $x$ on the left side. $$x = \frac{y}{3}$$ The subject is $\boxed{x = \frac{y}{3}}$. 5) Given formula: $y = \frac{x}{4}$. Make $x$ the subject. Step 1: Multiply both sides of the equation by 4. $$y \times 4 = \frac{x}{4} \times 4$$ $$4y = x$$ Step 2: Rewrite with $x$ on the left side. $$x = 4y$$ The subject is $\boxed{x = 4y}$. 6) Given formula: $b = ac$. Make $a$ and $c$ the subject. a) Make $a$ the subject: Step 1: Divide both sides of the equation by $c$. $$\frac{b}{c} = \frac{ac}{c}$$ $$\frac{b}{c} = a$$ Step 2: Rewrite with $a$ on the left side. $$a = \frac{b}{c}$$ The subject is $\boxed{a = \frac{b}{c}}$. b) Make $c$ the subject: Step 1: Divide both sides of the equation by $a$. $$\frac{b}{a} = \frac{ac}{a}$$ $$\frac{b}{a} = c$$ Step 2: Rewrite with $c$ on the left side. $$c = \frac{b}{a}$$ The subject is $\boxed{c = \frac{b}{a}}$. 7) Given formula: $n = 5ax$. Make $a$ and $x$ the subject. a) Make $a$ the subject: Step 1: Divide both sides of the equation by $5x$. $$\frac{n}{5x} = \frac{5ax}{5x}$$ $$\frac{n}{5x} = a$$ Step 2: Rewrite with $a$ on the left side. $$a = \frac{n}{5x}$$ The subject is $\boxed{a = \frac{n}{5x}}$. b) Make $x$ the subject: Step 1: Divide both sides of the equation by $5a$. $$\frac{n}{5a} = \frac{5ax}{5a}$$ $$\frac{n}{5a} = x$$ Step 2: Rewrite with $x$ on the left side. $$x = \frac{n}{5a}$$ The subject is $\boxed{x = \frac{n}{5a}}$. 8) Given formula: $\frac{x}{y} = 9$. Make $x$ the subject. Step 1: Multiply both sides of the equation by $y$. $$\frac{x}{y} \times y = 9 \times y$$ $$x = 9y$$ The subject is $\boxed{x = 9y}$. Send me the next one 📸