Question

Solvethefollowing:a) 7 − 4 + 12 = 2 + 8b) 14 + 15 − 9 + 1 = −7 + 1 − 9c) 4 − 10 = 8( + 2)

Answer 1

(a)

$7x-4x+12=2x+8$

First, we subtract 2x on each side.

$\begin{gathered} 7x-4x-2x+12=2x-2x+8 \\ x+12=8 \end{gathered}$

Then, we subtract 12 on each side.

$\begin{gathered} x+12-12=8-12 \\ x=-4 \end{gathered}$

The solution is -4.

(b)

$14x+15x-9+1=-7x+1-9$

We sum 7x on each side.

$\begin{gathered} 14x+15x+7x-9+1=-7x+7x+1-9 \\ 36x-8=-8 \end{gathered}$

Then, we add 8 on each side.

$\begin{gathered} 36x-8+8=-8+8 \\ 36x=0 \end{gathered}$

At last, we divide the equation by 36.

$\begin{gathered} \frac{36x}{36}=\frac{0}{36} \\ x=0 \end{gathered}$

The solution is 0.

(c)

$4x-10=8(x+2)$

First, we use the distributive property.

$4x-10=8x+16$

Then, we subtract 8x on each side.

$\begin{gathered} 4x-8x-10=8x-8x+16 \\ -4x-10=16 \end{gathered}$

Now, we add 10 on each side.

$\begin{gathered} -4x-10+10=16+10 \\ -4x=26 \end{gathered}$

At last, we divide the equation by -4.

$\begin{gathered} \frac{-4x}{-4}=\frac{26}{-4} \\ x=-6.5 \end{gathered}$

The solution is -6.5.