Question

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Answer 1

Explanation:

let : the pair of jeans = X

a. the equation is :

4(X-3) + 8 = 92

b. 4(X-3) = 92-8

4X -12 = 84

4X = 84+12

4X = 96

X = 96/4

X = 24

so, the price of each pair of jeans = $24

_________

For the solution x = 2.6, the left side of equation

(2x - 6) => would be 2(2.6)-6 = 5.2-6 = -8 ( the negative value),

but on the right side of the equation 4x+8 => 4(2.6) +8 = 18.4 ( the positive value)

this difference indicates that x=2.6 is not the right solution.

Answer 2

a) Let x be the cost of one pair of jeans

`4(x-3)+8=92`

b) $24

Explanation:

Given information:

• Cost of t-shirt = $8
• Coupon used for $3 off each pair of jeans
• Total spend = $92 (before tax)

Define the variable:

Let x = the cost of one pair of jeans

Create an equation using the defined variable and the given information:

• Apply the coupon ⇒ cost of one pair of jeans = (x - 3)
• 4 pairs of jeans ⇒ 4(x - 3)
• Plus the cost of the t-shirt ⇒ + 8
• Equals the total cost of ⇒ = 92:

`4(x-3)+8=92`

To find the price of each pair of jeans, solve the equation for x:

`\implies 4(x-3)+8=92`

`\implies 4(x-3)+8-8=92-8`

`\implies 4(x-3)=84`

`\implies (4(x-3))/(4)=(84)/(4)`

`\implies x-3=21`

`\implies x-3+3=21+3`

`\implies x=24`

Therefore, the price of each pair of jeans was $24.

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Solving 3(2x - 6) = 4x + 8 mentally:

Expand the brackets:

⇒ 16x - 18 = 4x + 8

Subtract 4x from both sides:

⇒ 12x - 18 = 8

Add 18 to both sides:

⇒ 12x = 26

Two times 12 is 24. As 26 is very close to 24, then x ≈ 2.

(The actual value of x is 2.2 to 2 decimal places).

Assessing the student's solution:

As x = 2.6 rounds to x ≈ 3 then the student's solution is incorrect because:

⇒ 3(2(3) - 6) = 4(3) + 8

⇒ 3(6 - 6) = 12 + 8

⇒ 3(0) = 20

⇒ 0 = 20