Equivalent Equations

3(4x+5)

3(4x-6)

4(4x-3)

4(3x-4)

8x-(4⋅4)+4x

 $3\left(x+6\right)=4x+7$  

 $3x=4x+7$  

 $3x+18=4x+7$  

 $18=x+7$  

Adding 3 to both sides of Equation A gives  $x+7=-8$  

Applying the distributive property to Equation A gives  $x+7=-8$  

Subtracting  3 from both sides of Equation A gives  $x+7=-8$  

Dividing both sides of Equation A by -3 gives  $x+7=-8.$  

It just is.

If you multiply both sides of  $x+4=20$  by 5, you get  $5\left(x+4\right)=100$  .

Because  $5x+4=100$  .

The equations are just equivalent.

 $35x=45$  

 $5x=75$  

 $5\left(x+30\right)=45$  

 $5\left(x+6\right)=45$  

$d=2\left(s+5\right)$

$d-5=2s$

$d-2=s+5$

$\frac{d}{2}=s+5$

 $2x=10$  

 $2x=20$  

 $2\left(x-5\right)=15$  

 $2x-20=0$  

 $4x-10=30$