Question

How do you solve `|7+ 7r | + 5= 40`?

Answer 1

Answer: `r = -6, 4`

Explanation:

`abs(7 + 7r) + 5 = 40`

`abs(7 + 7r) = 35`

`7 + 7r = +- 35`

`7 + 7r = + 35 => r = 28/7 = 4`

`7 + 7r = - 35 => r = -42/7 = -6`

Answer 2

`r=-6" or "r=4`

Explanation:

`"subtract 5 from both sides"`

`rArr|7+7r|=35`

`"the expression inside the absolute value can be positive"`
`"or negative"`

`color(magenta)"Positive expression"`

`rArr7+7r=35larrcolor(blue)"subtract 7 from both sides"`

`rArr7r=28larrcolor(blue)"divide both sides by 7"`

`rArrr=4`

`color(magenta)"Negative expression"`

`-7-7r=35larrcolor(blue)"add 7 to both sides"`

`rArr-7r=42larrcolor(blue)"divide both sides by "-7`

`rArrr=-6`

`color(blue)"As a check"`

`r=4rArr|35|+5=35+5=40color(white)(x)✔︎`

`r=-6rArr|-35|+5=35+5=40color(white)(x)✔︎`

`rArrx=-6" or "x=4" are the solutions"`