Question

4/5x = -16

Solve for x. -3x + 4 = 31

Solve for x.
2x + -12 = -22

What is the solution?
25 = 15 – 5r

What is the solution to the equation?
12.5 + 5x = -10

Answer 1

Hello!

The answers are:

1  $x=-20$

2  $x=-9$

3 $x=-5$ 

4  $r=-2$

5  $x=-4.5$

Why?

To know the solution of the problems, we need to isolate each variable.

Remember that:

- If we have an equality: if the number is subtracting (negative sign), and if you need to move it to the other side of the equality, its sign changes to positive.

- If we have an equality: if the number is adding (positive sign), and if you need to move it to the other side of the equality, its sign changes to negative.

- If we have  an equality:  if the number is part of a product , and if you need to move it to the other side of the equality, the same number will be dividing the factors of the side. On the opposite, if the number is dividing, it will be multiplying on the other side of the equality.

So,

1 - Solving for "x"

$\frac{4}{5}x=-16\\x=\frac{-16}{\frac{4}{5} }=-16*\frac{5}{4}=-20\\x=-20$

2 - Solving for "x"

$-3x+4=31\\-3x=31-4=27\\x=\frac{27}{-3}=-9$

3 - Solving for "x"

$2x+(-12)=-22\\2x-12=-22\\2x=-22+12=-10\\\\2x=-10\\x=\frac{-10}{2}=-5$

4  - Finding the solution

$25=15-5r\\25-15=-5r\\-5r=10\\r=\frac{10}{-5}=-2$

5 - Finding the solution

$12.5+5x=-10\\5x=-10-12.5=-22.5\\5x=-22.5\\x=\frac{-22.5}{5}=-4.5$

Have a nice day!

Answer 2

Answer:

$\large\boxed{Q1.\ x=-20}\\\boxed{Q2.\ x=-9}\\\boxed{Q3.\ x=-5}\\\boxed{Q4.\ r=-2}\\\boxed{Q5.\ x=-4.5}$

Step-by-step explanation:

$Q1:\\\dfrac{4}{5}x=-16\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{4}{5\!\!\!\!\diagup_1}x=(5)(-16)\\\\4x=-80\qquad\text{divide both sides by 4}\\\\\dfrac{4x}{4}=\dfrac{-80}{4}\\\\\boxed{x=-20}\\=======================$

$Q2:\\-3x+4=31\qquad\text{subtract 4 from both sides}\\\\-3x+4-4=31-4\\\\-3x=27\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3x}{-3}=\dfrac{27}{-3}\\\\\boxed{x=-9}\\=======================$

$Q3:\\2x-12=-22\qquad\text{add 12 to both sides}\\\\2x-12+12=-22+12\\\\2x=-10\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-10}{2}\\\\\boxed{x=-5}\\=======================$

$Q4:\\25=15-5r\qquad\text{subtract 15 from both sides}\\\\25-15=15-15-5r\\\\10=-5r\qquad\text{divide both sides by (-5)}\\\\\dfrac{10}{-5}=\dfrac{-5r}{-5}\\\\-2=r\to\boxed{r=-2}\\=======================$

$Q5:\\12.5+5x=-10\qquad\text{subtract 12.5 from both sides}\\\\12.5-12.5+5x=-10-12.5\\\\5x=-22.5\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{-22.5}{5}\\\\\boxed{x=-4.5}$