Question

please do the steps Solve for d: 1/6d-8=5/8 2. Solve for x: 3x-4+5x=10-2z 3. Solve for c: 7(c-3)=14 4. Solve for m: 11(m/22+3/44)=87m+m 5. Solve for k: ck+5k=a

Answer 1

d = 55.5

x = 1

c = 11

m =
`(1)/(122)`

k =
`(a)/((c + 5))`

Explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

`(1)/(6)`d - 8 =
`(5)/(8)` x 2

Step 1. Simplify.

`(5)/(8)` x 2 =
`(5)/(8)` x
`(2)/(1)` =
`(10)/(8)`

Step 2. Cancel out the negative 8.

`(1)/(6)`d - 8 =
`(10)/(8)`

+ 8 to both sides (do the opposite:
`(1)/(6)`d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

`(1)/(6)`d =
`(10)/(8)` + 8

Step 3. Simplify.

`(10)/(8)` + 8 =
`(10)/(8)` +
`(8)/(1)` =
`(10)/(8)` +
`(64)/(8)` =
`(74)/(8)` =
`(37)/(4)`

Step 4. Cancel out the
`(1)/(6)`.

`(1)/(6)`d =
`(37)/(4)`

÷
`(1)/(6)` from both sides (do the opposite: d is multiplied by
`(1)/(6)` right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷
`(1)/(6)` = x 6

So....

x 6 to both sides

d =
`(37)/(4)` x 6 =
`(37)/(4)` x
`(6)/(1)` =
`(222)/(4)` =
`(111)/(2)` = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11(
`(m)/(22)` +
`(3)/(44)`) = 87m + m × 5

Step 1. Expand the brackets

11(
`(m)/(22)` +
`(3)/(44)`) = (11 x
`(m)/(22)`) + (11 x
`(3)/(44)`) = (
`(11)/(1)` x
`(m)/(22)`) + (
`(11)/(1)` x
`(3)/(44)`) =
`(11m)/(22)` +
`(33)/(44)` =
`(m)/(2)` +
`(3)/(4)`

Step 2. Simplify.

87m + m x 5 = 87m + 5m = 92m

Step 3. Cancel out the add
`(3)/(4)`

`(m)/(2)` +
`(3)/(4)` = 92m

-
`(3)/(4)`

`(m)/(2)` = 92m -
`(3)/(4)`

`(m)/(2)` =
`(92m)/(1)` -
`(3)/(4)`

`(m)/(2)` =
`(368m)/(4)` -
`(3)/(4)`

`(m)/(2)` =
`(368m - 3)/(4)`

Step 4. Cancel out the ÷ 4

`(m)/(2)` =
`(368m - 3)/(4)`

x 4

2m = 368m - 3

Step 5. Cancel out the 368m

2m = 368m - 3

- 368m

-366m = - 3

Step 6. Cancel out the × -366

-366m = -3

÷ -366

m =
`(-3)/(-366)`

m =
`(1)/(122)`

Step 7. Write down your answer.

m =
`(1)/(122)`

Q5.

ck + 5k = a

Step 1. Factorise

ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)

Step 2. Cancel out the × (c + 5)

k(c + 5) = a

÷ (c + 5)

k = a ÷ (c + 5)

k =
`(a)/((c + 5))`