Question

literal equations homework
name:
date: due date: per:
directions: solve for the indicated variable. show all steps in the process.

1. solve for y:

$y - 3x = 5$

1. volume of a prism: solve for w

$v = lwh$

1. solve for m;

$\frac{m + k}{h} = w$

1. solve for m;

$e = mc^2$

1. solve for y:

$3y - 9x = -33$

1. solve for c:

$bx + cy = d$

1. solve for s:

$r = \frac{cs}{d}$

1. solve for x:

$3m = 2(4 + x)$

1. solve for p:

$ap - b = r$

1. solve for z:

$d = z(a - b) + c$
isolate y:
$2x + 5y = 3$

1. solve for k:

$h = \frac{1}{6}k - w$
score: ____ out of ____

Explanation:

1. Solve for $y$:

Step1: Isolate $y$ by adding $3x$

$y - 3x + 3x = 5 + 3x$

Step2: Simplify to get $y$

$y = 3x + 5$

2. Solve for $w$:

Step1: Isolate $w$ by dividing by $lh$

$\frac{V}{lh} = \frac{lwh}{lh}$

Step2: Simplify to get $w$

$w = \frac{V}{lh}$

3. Solve for $m$:

Step1: Eliminate denominator by multiplying by $h$

$\frac{m+k}{h} \times h = w \times h$

Step2: Isolate $m$ by subtracting $k$

$m + k - k = wh - k$

Step3: Simplify to get $m$

$m = wh - k$

4. Solve for $m$:

Step1: Isolate $m$ by dividing by $c^2$

$\frac{E}{c^2} = \frac{mc^2}{c^2}$

Step2: Simplify to get $m$

$m = \frac{E}{c^2}$

5. Solve for $y$:

Step1: Isolate $3y$ by adding $9x$

$3y - 9x + 9x = -33 + 9x$

Step2: Divide by 3 to solve for $y$

$\frac{3y}{3} = \frac{9x - 33}{3}$

Step3: Simplify to get $y$

$y = 3x - 11$

6. Solve for $c$:

Step1: Isolate $cy$ by subtracting $bx$

$bx + cy - bx = d - bx$

Step2: Isolate $c$ by dividing by $y$

$\frac{cy}{y} = \frac{d - bx}{y}$

Step3: Simplify to get $c$

$c = \frac{d - bx}{y}$

7. Solve for $S$:

Step1: Eliminate denominator by multiplying by $D$

$R \times D = \frac{CS}{D} \times D$

Step2: Isolate $S$ by dividing by $C$

$\frac{RD}{C} = \frac{CS}{C}$

Step3: Simplify to get $S$

$S = \frac{RD}{C}$

8. Solve for $x$:

Step1: Expand the right-hand side

$3m = 8 + 2x$

Step2: Isolate $2x$ by subtracting 8

$3m - 8 = 2x$

Step3: Divide by 2 to solve for $x$

$\frac{3m - 8}{2} = x$

Step4: Simplify to get $x$

$x = \frac{3m}{2} - 4$

9. Solve for $p$:

Step1: Isolate $ap$ by adding $b$

$ap - b + b = r + b$

Step2: Isolate $p$ by dividing by $a$

$\frac{ap}{a} = \frac{r + b}{a}$

Step3: Simplify to get $p$

$p = \frac{r + b}{a}$

10. Solve for $z$:

Step1: Isolate $z(a-b)$ by subtracting $c$

$d - c = z(a - b) + c - c$

Step2: Isolate $z$ by dividing by $(a-b)$

$\frac{d - c}{a - b} = \frac{z(a - b)}{a - b}$

Step3: Simplify to get $z$

$z = \frac{d - c}{a - b}$

11. Isolate $y$:

Step1: Isolate $5y$ by subtracting $2x$

$2x + 5y - 2x = 3 - 2x$

Step2: Divide by 5 to solve for $y$

$\frac{5y}{5} = \frac{3 - 2x}{5}$

Step3: Simplify to get $y$

$y = \frac{3 - 2x}{5}$

12. Solve for $k$:

Step1: Isolate $\frac{1}{6}k$ by adding $w$

$h + w = \frac{1}{6}k - w + w$

Step2: Multiply by 6 to solve for $k$

$(h + w) \times 6 = \frac{1}{6}k \times 6$

Step3: Simplify to get $k$

$k = 6(h + w)$

Answer:

1. $y = 3x + 5$
2. $w = \frac{V}{lh}$
3. $m = wh - k$
4. $m = \frac{E}{c^2}$
5. $y = 3x - 11$
6. $c = \frac{d - bx}{y}$
7. $S = \frac{RD}{C}$
8. $x = \frac{3m}{2} - 4$
9. $p = \frac{r + b}{a}$
10. $z = \frac{d - c}{a - b}$
11. $y = \frac{3 - 2x}{5}$
12. $k = 6(h + w)$