Question

What is the solution to the equation? 1../ 13.5 + 5x = 20

What is the solution to the equation? 2..//-14x + 16 = -12

Solve for x.
-32x – 18 = -2

Solve for x.
4 + x/5 = -3

Answer 1

Answer:

1. $x=1.3$

2. $x=2$

3. $x=-\frac{1}{2}$

4. $x=-35$

Step-by-step explanation:

1. For the equation $13.5 + 5x = 20$, subtract 13.5 from both sides of the equation:

$13.5 + 5x -13.5= 20-13.5\\5x=6.5$

And divide both sides by 5:

$\frac{5x}{5}=\frac{6.5}{5}\\\\x=1.3$

2. For the equation $-14x + 16 = -12$, subtract 16 from both sides of the equation:

$-14x + 16 -16= -12-16\\-14x=-28$

And divide both sides by -14:

$\frac{-14x}{-14}=\frac{-28}{-14}\\\\x=2$

3. For the equation $-32x - 18 = -2$, add 18 to both sides of the equation:

$-32x - 18+18 = -2+18\\-32x=16$

And divide both sides by -32:

$\frac{-32x}{-32}=\frac{16}{-32}\\\\x=-\frac{1}{2}$

4. For the equation  $4 + \frac{x}{5}= -3$ subtract 4 from both sides of the equation:

$4 + \frac{x}{5}-4= -3-4\\\\\frac{x}{5}=-7$

And multiply both sides by 5:

$(5)(\frac{x}{5})=-7(5)\\\\x=-35$

Answer 2

Hello!

The answers are:

1 $1.3$

2  $2$

3 $x=-\frac{1}{2}$

4 $x=-35$

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 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 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 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.

So,

1 -

$13.5+5x=20\\5x=20-13.5=6.5\\x=\frac{6.5}{5}\\x=1.3$

2 -

$-14x+16=-12\\16+12=14x\\14x=16+12\\14x=28\\x=\frac{28}{14}=2$

3 - Solving for "x"

$-32x-18 = -2\\-18+2=32x\\32x=-18+2=-16\\32x=-16\\x=\frac{-16}{32}=-\frac{1}{2}$

4 - Solving for "x"

$4+\frac{x}{5}=-3\\\frac{x}{5}=-3-4\\\frac{x}{5}=-7\\x=(-7)*(5)=-35$

Have a nice day!