Question

For each equation write a situation that matches it (annotate the equation to show how each part is modelled in the situation) and then solve the equation and give the answer in a complete sentence.1) 2(8a + 1) = 1144) −128 = −8(6 + 5x)2) −8(3 − 7x) = 885) 8(2 − 6p) + 3(p + 8) = −503) 6(k + 6) = 846) −24 = 4(4x + 4) − 4(8 + 3x)

Answer 1

We are given a number (it can be both a positive or a negative number) and we are told that if we subtract 7 times this number from 3 and then multiply the result by -8 we are going to get 88. What is this mysterious number?

This situation can be translated to

`-8(3-7x)=88`

How do we then solve for x, the mysterious number?

Let us divide both sides of the equation by -8, this gives

`(-1)/(8)*-8(3-7x)=88*(-1)/(8)`
`\rightarrow3-7x=-(88)/(8)`
`3-7x=-10`

And now let us add 7x to both sides

`3=-10+7x`

and then add 10 to both sides to get

`13=7x`

and finally, dividing both sides by 7 gives

`\textcolor{#FF7968}{x=(13)/(7)\approx1.86}`

which is our answer!