Question

1. equations and expressions score __/13 or __%

a. simplify these expressions

1. $3a + 7 + 6a =$ _____________ 2. $\frac{8a - 12b}{4} =$ ___________

score__/2 or __%
b. solve the equations to find the value of the variable. score__/8 or __%
$24 = x + 3$ $18 = x - 12$ $4x = 16$ $4 = x/5$
score: score: score: score:
$20 = 2x + 6$ $3x - 11 = 34$ $56 = x/2 + 6$ $45 = x/3 - 15$
score: score: score: score:
c. graphing: use this equation to complete the following problems $y = 2x + 4$.

1. what is the y intercept of this line described by the given equation? ______
2. what is the slope of the line described by the given equation? ______
3. graph the line described by the given equation on the coordinate plane below.

score __/3 or __%

Explanation:

Part A: Simplify Expressions

Step1: Combine like terms

$3a + 6a + 7 = 9a + 7$

Step2: Split fraction, simplify each term

$\frac{8a}{4} - \frac{12b}{4} = 2a - 3b$

Part B: Solve Equations

Step1: Isolate x, subtract 3

$24 = x + 3 \implies x = 24 - 3 = 21$

Step2: Isolate x, add 12

$18 = x - 12 \implies x = 18 + 12 = 30$

Step3: Isolate x, divide by 4

$4x = 16 \implies x = \frac{16}{4} = 4$

Step4: Isolate x, multiply by 5

$4 = \frac{x}{5} \implies x = 4 \times 5 = 20$

Step5: Isolate x term, subtract 6

$20 = 2x + 6 \implies 2x = 20 - 6 = 14$

Step6: Solve for x, divide by 2

$x = \frac{14}{2} = 7$

Step7: Isolate x term, add 11

$3x - 11 = 34 \implies 3x = 34 + 11 = 45$

Step8: Solve for x, divide by 3

$x = \frac{45}{3} = 15$

Step9: Isolate x term, subtract 6

$56 = \frac{x}{2} + 6 \implies \frac{x}{2} = 56 - 6 = 50$

Step10: Solve for x, multiply by 2

$x = 50 \times 2 = 100$

Step11: Isolate x term, add 15

$45 = \frac{x}{3} - 15 \implies \frac{x}{3} = 45 + 15 = 60$

Step12: Solve for x, multiply by 3

$x = 60 \times 3 = 180$

Part C: Linear Graph Analysis

Step1: Identify y-intercept (form $y=mx+b$)

In $y=2x+4$, $b=4$, so y-intercept is 4

Step2: Identify slope (form $y=mx+b$)

In $y=2x+4$, $m=2$, so slope is 2

Step3: Plot line using intercept and slope

1. Plot y-intercept point $(0, 4)$
2. Use slope $\frac{2}{1}$: from $(0,4)$, move 1 right, 2 up to $(1,6)$; repeat to get $(2,8)$, or move left 1, down 2 to $(-1,2)$
3. Draw straight line through points

Answer:

Part A

1. $9a + 7$
2. $2a - 3b$

Part B

1. $x = 21$
2. $x = 30$
3. $x = 4$
4. $x = 20$
5. $x = 7$
6. $x = 15$
7. $x = 100$
8. $x = 180$

Part C

1. $4$
2. $2$
3. A straight line passing through points such as $(0,4)$, $(1,6)$, $(-1,2)$ plotted on the coordinate plane.