Question

1. isolate y: -3x = 4y + -29
2. solve for y: x = y(a + b) + 1
3. solve for z: t = \\(\frac{2}{3}z - 4\\)
4. solve for c: \\(\frac{a + b + c}{4} = k\\)

level 3 challenge

1. solve for c: f = \\(\frac{9}{5}c + 32\\)
2. solve for q: t = \\(\frac{v}{q}\\)
3. solve for \\(b_2\\): a = \\(\frac{1}{2}(b_1 + b_2)h\\) (with some handwritten work)
4. solve for r: v = \\(\frac{1}{3}\pi h^2(3r - h)\\)

solve for \\(y_2\\): m = \\(\frac{y_2 - y_1}{x_2 - x_1}\\)

Explanation:

12. Isolate $y$:

Step1: Isolate $4y$ term

$4y = -3x + 20$

Step2: Divide by 4

$y = \frac{-3x + 20}{4} = -\frac{3}{4}x + 5$

13. Solve for $y$:

Step1: Isolate $y(a+b)$ term

$x - 1 = y(a+b)$

Step2: Divide by $(a+b)$

$y = \frac{x - 1}{a+b}$

14. Solve for $x$:

Step1: Isolate $\frac{2}{3}x$ term

$t + 4 = \frac{2}{3}x$

Step2: Multiply by $\frac{3}{2}$

$x = \frac{3(t + 4)}{2} = \frac{3t}{2} + 6$

15. Solve for $c$:

Step1: Multiply both sides by 4

$a + b + c = 4k$

Step2: Isolate $c$

$c = 4k - a - b$

16. Solve for $C$:

Step1: Isolate $\frac{9}{5}C$ term

$F - 32 = \frac{9}{5}C$

Step2: Multiply by $\frac{5}{9}$

$C = \frac{5(F - 32)}{9}$

17. Solve for $Q$:

Step1: Multiply both sides by $Q$

$TQ = V$

Step2: Divide by $T$

$Q = \frac{V}{T}$

18. Solve for $b_2$:

Step1: Multiply by 2

$2A = (b_1 + b_2)h$

Step2: Divide by $h$

$\frac{2A}{h} = b_1 + b_2$

Step3: Isolate $b_2$

$b_2 = \frac{2A}{h} - b_1$

19. Solve for $r$:

Step1: Multiply by 3

$3V = \pi h^2(3r - h)$

Step2: Divide by $\pi h^2$

$\frac{3V}{\pi h^2} = 3r - h$

Step3: Isolate $3r$

$\frac{3V}{\pi h^2} + h = 3r$

Step4: Divide by 3

$r = \frac{V}{\pi h^2} + \frac{h}{3}$

Solve for $y_2$:

Step1: Multiply by $(x_2 - x_1)$

$m(x_2 - x_1) = y_2 - y_1$

Step2: Isolate $y_2$

$y_2 = m(x_2 - x_1) + y_1$

Answer:

1. $\boldsymbol{y = -\frac{3}{4}x + 5}$
2. $\boldsymbol{y = \frac{x - 1}{a+b}}$
3. $\boldsymbol{x = \frac{3t}{2} + 6}$
4. $\boldsymbol{c = 4k - a - b}$
5. $\boldsymbol{C = \frac{5(F - 32)}{9}}$
6. $\boldsymbol{Q = \frac{V}{T}}$
7. $\boldsymbol{b_2 = \frac{2A}{h} - b_1}$
8. $\boldsymbol{r = \frac{V}{\pi h^2} + \frac{h}{3}}$

Solve for $y_2$: $\boldsymbol{y_2 = m(x_2 - x_1) + y_1}$