When you have to solve an equation, you have to "isolate" the variable, so that it remains alone on the left hand side. If you have to get rid of added/subtracted terms you have to subtract/add, if you have to get rid of multiplied/divided terms you have to divide/multiply.
1: Divide both sides by 2 to get [tex]x=7[/tex]
2: Subtract 5 from both terms to get [tex]x=-27[/tex]
3: Multiply both sides by -11 to get [tex]x=-55[/tex]
4: Same as number 2.
5: Distribute the 5 to get [tex]5x+50=40[/tex]. Subtract 50 from both sides to get [tex]5x=-10[/tex]. Divide both sides by 5 to get [tex]x=-2[/tex]
6: Add 4 to both sides to get [tex]2x=12+5x[/tex]. Subtract [tex]5x[/tex] from both sides to get [tex]-3x=12[/tex]. Then, it's the same as number 1.
7: The symmetric property of equality. It states that if [tex]a=b[/tex], then [tex]b=a[/tex].
8: The transitive property of equality. It states that if [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex].
9: You must divide the number of people by the size of the teams: [tex]1008\div 6=168[/tex]
10: Let [tex]l[/tex] and [tex]w[/tex] be the length and width, respectively. We know that
[tex]l=w+67[/tex]
(the length is 67 more than the width), and that
[tex]2(l+w)=346[/tex]
(the perimeter is 346. We can simplify this equation into
[tex]l+w=173[/tex]
Now we substitute [tex]l=w+67[/tex] to get
[tex]w+67+w=173\iff 2w=106 \iff w=53[/tex]
And since the length is 67 more, we have
[tex]l=53+67=120[/tex]
