Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 3 Algebraic Linear Equations to finish your assignments.

## Math in Focus Grade 8 Course 3 A Chapter 3 Answer Key Algebraic Linear Equations

### Math in Focus Grade 8 Chapter 3 Quick Check Answer Key

**Explain why each pair of equations is equivalent or not equivalent.**

Question 1.

x + 4 = 10 and x – 1 = 3

Answer:

Not equivalent,

Explanation:

Given x + 4 = 10 and x-1 =3 means x = 3+1 =4,

if we substitute x = 4 in x + 4 = 4 + 4 = 8 ≠ 10,

so equations are not equivalent.

Question 2.

\(\frac{1}{5}\)x = 4 and x = 20

Answer:

Equivalent,

Explanation:

Given \(\frac{1}{5}\)x = 4 and x = 20 upon solving

\(\frac{1}{5}\)x = 4 we get x = 4 X 5 = 20 therefore

pair is equivalent as x = 20.

Question 3.

0.5x + 1 = 1.5x and 2x = 2

Answer:

Equivalent,

Explanation:

Given 0.5x +1 = 1.5x and 2x =2 means x= 2/2 equal to 1,

so 0.5 (1) + 1 = 1.5 X 1 is 0.5 +1 = 1.5 , So 1.5 = 1.5,therefore

both equations are equivalent.

Question 4.

2(x + 9) = 14 and 2(x – 7) = -18

Answer:

Equivalent,

Explanation:

Given 2(x -7) = -18 upon solving

2x – 14 = -18,

2x = -18+14,

2x = -4 therfore x = -4/2 = -2 now substituting

2(-2 -7) = – 4 -14 = -18 which is equal to – 18

So both equations are equivalent.

**Write a linear equation for each situation. State the independent and dependent variables for each equation.**

Question 5.

A manufacturer produces beverages in small and large bottles.

Each small bottle contains s liters of beverages.

Each large bottle contains t liters, which is 1 more liter than the

quantity in the small bottle. Express t in terms of s.

Answer:

t = (s + (sX1)) liters,

Explanation:

Given A manufacturer produces beverages in small and large bottles.

Each small bottle contains s liters of beverages.

Each large bottle contains t liters, which is 1 more liter than the

quantity in the small bottle. Expressing t in terms of s as t = (s + (sX1)) liters.

Question 6.

Hazel is 4 years younger than Alphonso. Express Alphonso’s age, a, in terms of Hazel’s age, h.

Answer:

h=(a-4),

Explanation:

Given Hazel is 4 years younger than Alphonso.

Expressing Alphonso’s age, a, in terms of Hazel’s age, h.

h=(a-4).

Question 7.

A bouquet of lavender costs $12. Find the cost, C, of n bouquets of lavender.

Answer:

C = $12n

Explanation:

Given a bouquet of lavender costs $12, the cost, C, of n bouquets of lavender is

c = $12 X n = $12n.

Question 8.

The distance, d miles, traveled by a bus is 40 times the time,t hours,

used for the journey. Find d in terms of t.

Answer:

d = 40t,

Explanation:

Given the distance, d miles, traveled by a bus is 40 times the time,t hours,

used for the journey is d = 40t.

**Solve each equation.**

Question 9.

4x = 14 + 2x

Answer:

x =7,

Explanation:

Given 4x = 14 + 2x, upon solving

4x – 2x = 14,

2x = 14,

x = 14/2 = 7.

Question 10.

\(\frac{1}{3}\)v = 2 – \(\frac{2}{9}\)v

Answer:

v = \(\frac{18}{5}\),

Explanation:

Given \(\frac{1}{3}\)v = 2 – \(\frac{2}{9}\)v,

\(\frac{1}{3}\)v = \(\frac{18 -2v}{9}\),

\(\frac{9}{3}\)v = 18 -2v,

3 v = 18 -2v,

5v = 18, therefore v = \(\frac{18}{5}\).

Question 11.

c + 2(1 – c) = 10 – 3c

Answer:

c = 4,

Explanation:

Given c + 2(1 – c) = 10 – 3c,

c + 2 – 2c = 10 -3c,

2 – c = 10 – 3c,

3c-c = 10-2,

2c = 8,

c = 4.

Question 12.

3(2 + 3x) = 13(x + 2)

Answer:

x = -5,

Explanation:

Given 3(2+3x) = 13(x +2) upon solving

6 + 9x = 13x + 26,

6-26 = 13x – 9x,

-20 = 4 x,

x = -5.

**Write the decimal for each fraction. Use bar notation.**

Question 13.

\(\frac{3}{18}\)

Answer:

Explanation:

A bar notation, which is a way to show repeating numbers after a decimal point,

here when 3 divides by 18 we get 0.166666 where 6 is repeating so we keep a bar on 6

as shown above.

Question 14.

\(\frac{14}{99}\)

Answer:

Explanation:

When 14 divides by 99 we get 0.14141414 where 14 is repeating so we keep a bar on 14

as shown above.

Question 15.

\(\frac{13}{12}\)

Answer:

Explanation:

When 13 divides by 12 we get 1.083333 where 3 is repeating so we keep a bar on 3

as shown above.

Question 16.

\(\frac{5}{27}\)

Answer:

Explanation:

When 5 divides by 27 we get 0.185185 where 185 is repeating so we keep a bar on 185

as shown above.