Question

The product of 8/9 and the sum of a number and – 4 is less than or equal to 64.

What are all the possible values of the number? Show your work.

Answer 1

Let the number be x

ATQ,

`\sf (8)/(9) (x - 4) \leqslant 64`

Note that

• Product means ×
• Sum means +
• Less than or equal to means ≤

Solve the equation for x ~

`\sf \: x - 4 \leqslant 72`

`\sf \: x \leqslant 72 + 4`

`\boxed{ \tt \: x \leqslant 76}`

Answer 2

`x\leq 76`

Explanation:

Let x = unknown number

`\implies \frac89 * (x-4)\leq 64`

`\implies (8(x-4))/(9)\leq 64`

Multiply both sides by 9:

`\implies 8(x-4)\leq 576`

Expand brackets:

`\implies 8x-32\leq 576`

Add 32 to both sides:

`\implies 8x\leq 608`

Divide both sides by 8:

`\implies x\leq 76`