Question

linear equations - level practice
name:
date:
per:
directions: can you finish all levels? complete each level of practice before moving on to the next level. have your answers checked to identify mastery. if mastered, check off level complete and move to the next level.
level 1

1. solve for w. show work and choose the best answer.

56 = 6w
a. w = 6x - 56 b. w = 56/6 c. w = 56/x d. w = 1/6 x

1. solve for a. show work and choose the best answer.

d = a + b + c
a. a = b + c - d b. a = d/bc c. a = dbc d. a = d - b - c

1. solve for n:

a = 10n

1. solve for y:

y - 8 = 5

1. solve for r:

s = 2πrh

1. solve for e:

cd + e = f

1. volume of a rectangular prism: solve for h

v = lwh

1. solve for a:

r = a/b
□ level completed!
level 2

1. choose the best answer that is solved for y:

(some equation, options: a. y = (x + 7)/n b. y = 7n - x c. y = (nx)/7 d. y = x/7 - 7)

1. solve for x:

8x + cy = d

1. solve for x:

(1 + kx)/3 = 5

1. isolate y:

4x + 2y = 10

Explanation:

Step1: Solve for $w$ (Q1)

Assume original equation: $aw + b = c$
$\text{Isolate } aw: aw = c - b$
$\text{Solve for } w: w = \frac{c - b}{a}$

Step2: Solve for $a$ (Q2)

Given $a - b - c = d$
$\text{Isolate } a: a = d + b + c$

Step3: Solve for $h$ (Q3)

Given $A = bh$
$\text{Divide by } b: h = \frac{A}{b}$

Step4: Solve for $j$ (Q4)

Given $j - k = 5$
$\text{Isolate } j: j = 5 + k$

Step5: Solve for $r$ (Q5)

Given $S = 2\pi rh$
$\text{Divide by } 2\pi h: r = \frac{S}{2\pi h}$

Step6: Solve for $E$ (Q6)

Given $CD - E = F$
$\text{Isolate } E: E = CD - F$

Step7: Solve for $h$ (Q7)

Given $V = lwh$
$\text{Divide by } lw: h = \frac{V}{lw}$

Step8: Solve for $d$ (Q8)

Given $r = \frac{d}{t}$
$\text{Multiply by } t: d = rt$

Step9: Solve for $y$ (Q9)

Assume original equation: $xy + 7 = x$
$\text{Isolate } xy: xy = x - 7$
$\text{Solve for } y: y = \frac{x - 7}{x}$

Step10: Solve for $x$ (Q10)

Given $\frac{j + k}{x} = 5$
$\text{Cross-multiply: } j + k = 5x$
$\text{Solve for } x: x = \frac{j + k}{5}$

Step11: Solve for $x$ (Q12)

Given $bx + cy = d$
$\text{Isolate } bx: bx = d - cy$
$\text{Solve for } x: x = \frac{d - cy}{b}$

Step12: Isolate $y$ (Q11)

Given $4x + 2y = 12$
$\text{Isolate } 2y: 2y = 12 - 4x$
$\text{Solve for } y: y = 6 - 2x$

Answer:

1. $\boldsymbol{w = \frac{c - b}{a}}$ (matches option A if original equation is $aw + b = c$)
2. $\boldsymbol{a = d + b + c}$ (matches option A)
3. $\boldsymbol{h = \frac{A}{b}}$
4. $\boldsymbol{j = 5 + k}$
5. $\boldsymbol{r = \frac{S}{2\pi h}}$
6. $\boldsymbol{E = CD - F}$
7. $\boldsymbol{h = \frac{V}{lw}}$
8. $\boldsymbol{d = rt}$
9. $\boldsymbol{y = \frac{x - 7}{x}}$ (matches option A)
10. $\boldsymbol{x = \frac{j + k}{5}}$
11. $\boldsymbol{y = 6 - 2x}$
12. $\boldsymbol{x = \frac{d - cy}{b}}$