Respuesta :
The addition property of equality:
1) If a=b then a+c=b+c.
For example a=b=3 and c=4, replace a=b=3 and c=4 in a+c=b+c, we get
3+4=3+4=7.
2) If a=b, and c=d, then a+c=b+d
For example a=b=3 and c=d=5, replace a=b=3 and c=d=5 in a+c=b+d, we get
3+5=3+5=8.
The subtraction property of equality
1) If a=b then a-c=b-c.
For example a=b=3 and c=4, replace a=b=3 and c=4 in a-c=b-c, we get
3-4=3-4=-1.
2) If a=b, and c=d, then a+c=b+d.
For example a=b=3 and c=d=5, replace a=b=3 and c=d=5 in a-c=b-d, we get
3-5=3-5=-2.
The multiplication property of equality
1) If a=b then ac=bc.
2) If a=b, and c=d, then ac=bd.
The division property of equality
[tex]\text{ If a=b and c}\ne0,\text{ then }\frac{a}{c}=\frac{b}{c}[/tex][tex]\text{ If a=b and c=d}\ne0,\text{ then }\frac{a}{c}=\frac{b}{d}[/tex]Simplifying or the substitution property
If a=b, then a can be substituted for b in any equation.
The distributive property
[tex]a\times(b+c)=(a\times b)+(a\times c)[/tex][tex](a+b)\times c=(a\times c)+(b\times c)[/tex]Example problem:
Solve : 4x-8=2(x+8).
[tex]4x-8=2x+16\text{ by distributive property}[/tex][tex]2x-8=16\text{ by subtraction property here c=}2x[/tex][tex]2x=24\text{ by addition property here c=}8[/tex][tex]x=12\text{ by division property here c=2}[/tex]