The answer is: [C]: " <span>{x | x > 5} " .
</span><span>__________________________________________
Explanation:
__________________________________________
Given: " 4(x </span>− 3) − 2(x − <span>1) > 0 " ;
__________________________________________
Note the "distributive property of multiplication" :
__________________________________________
a(b+c) = ab + ac ;
a(b</span>−c) = ab −<span> ac ;
___________________________________________
So, given:
_________________________________________________
</span> → 4(x − 3) − 2(x − 1) > 0 ;
<span>_________________________________________________
Let us simplify; and rewrite:
_________________________________________________
Start with:
______________________________________________________
</span>→<span> -2 (x </span>− 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;
<span>______________________________________________________
Now, continue with:
</span> → 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;
<span>______________________________________________________
</span><span>So, given the original problem:
______________________________________________________
</span> → 4(x − 3) − 2(x − 1) > 0 ;
<span>______________________________________________________
Rewrite;
Replacing: "4</span>(x − 3)" ; with: "4x − 12" ;
and replacing "− 2(x − 1)" ; with: " -2x + 2" ;
<span>______________________________________________________
as follows: </span>→ " 4x − 12 − 2x + 2 " > 0 ;
______________________________________________________
On the "left-hand side", combine the "like terms", and simplify ;
______________________________________________________
+4x −2x = +2x ; −12 +2 = -10 ; and rewrite:
<span>______________________________________________________
</span>→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;
<span>______________________________________________________
</span>→ 2x − 10 + 10 > 0 + 10 ;
<span>______________________________________________________
to get: </span>→ 2x > 10 ;
<span>______________________________________________________
</span>→<span> Now, divide EACH SIDE of the inequality by "2";
to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;
_______________________________________________________
</span>→ 2x / 2 > 10 / 2 ;
<span>_______________________________________________________
</span>→ x > 5 ; which is:
_______________________________________________________
→ Answer choice: [C]: " {x | x > 5} " .
_______________________________________________________
</span><span>__________________________________________
Explanation:
__________________________________________
Given: " 4(x </span>− 3) − 2(x − <span>1) > 0 " ;
__________________________________________
Note the "distributive property of multiplication" :
__________________________________________
a(b+c) = ab + ac ;
a(b</span>−c) = ab −<span> ac ;
___________________________________________
So, given:
_________________________________________________
</span> → 4(x − 3) − 2(x − 1) > 0 ;
<span>_________________________________________________
Let us simplify; and rewrite:
_________________________________________________
Start with:
______________________________________________________
</span>→<span> -2 (x </span>− 1) = (-2*x) − (-2 *1) = -2x − (-2) = -2x + 2 ;
<span>______________________________________________________
Now, continue with:
</span> → 4(x − 3) = (4*x) − (4*3) = 4x − 12 ;
<span>______________________________________________________
</span><span>So, given the original problem:
______________________________________________________
</span> → 4(x − 3) − 2(x − 1) > 0 ;
<span>______________________________________________________
Rewrite;
Replacing: "4</span>(x − 3)" ; with: "4x − 12" ;
and replacing "− 2(x − 1)" ; with: " -2x + 2" ;
<span>______________________________________________________
as follows: </span>→ " 4x − 12 − 2x + 2 " > 0 ;
______________________________________________________
On the "left-hand side", combine the "like terms", and simplify ;
______________________________________________________
+4x −2x = +2x ; −12 +2 = -10 ; and rewrite:
<span>______________________________________________________
</span>→ 2x − 10 > 0 ; Add "10" to EACH SIDE of the inequality;
<span>______________________________________________________
</span>→ 2x − 10 + 10 > 0 + 10 ;
<span>______________________________________________________
to get: </span>→ 2x > 10 ;
<span>______________________________________________________
</span>→<span> Now, divide EACH SIDE of the inequality by "2";
to isolate "x" on one side of the inequality; & to "solve"/"simply" for "x" ;
_______________________________________________________
</span>→ 2x / 2 > 10 / 2 ;
<span>_______________________________________________________
</span>→ x > 5 ; which is:
_______________________________________________________
→ Answer choice: [C]: " {x | x > 5} " .
_______________________________________________________
5
0