Answer:
9 + 2j is the required algebraic equation.
Answer:
d
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
y - y1 = m (x - x1)
y1 = 3
x1 = 5
m(the slope)= -12
Answer:
D All positive integers are rational numbers.
Step-by-step explanation:
Integers are rational numbers
The answer: " x = ⅓ " .
____________________________________________________
Given: " 3x − 2 (x + 3) = 4x −<span> 7 " ; Solve for "x" ;
____________________________________________________
Start with the following term on the "left-hand side" of the equation:
" - 2 (x + 3) " ;
____________________________________________________
Note the "distributive property of multiplication" :
____________________________________________________
a(b + c) = ab + ac ;
a(b </span>− c) = ab <span>− ac ;
____________________________________________________
As such,
" -2 (x + 3) = -2(x) + -2(3) = -2x + (-6) = -2x </span>− 6 ;
____________________________________________________
So, we can rewrite our equation:
____________________________________________________
" 3x − 2 (x + 3) = 4x − 7 " ; substituting: " -2x − 6" (for " −2 (x + 3)" ; as follows:
____________________________________________________
3x − 2x − 6 = 4x − 7 ;
___________________________________________________
On the left-hand side off the equation;
________________________________
We can combine the "like terms" ; as follows:
3x − 2x = 1x = x ; and rewrite the equation:
__________________________________
x − 6 = 4x − 7 ;
____________________________________
We can subtract "4x" from each side of the equation; and add "6" to each side of the equation:
____________________________________
x − 6 − 4x + 6 = 4x − 7 − 4x + 6 ;
to get: -3x = -1 ;
____________________________________
Now, we divide EACH SIDE of the equation by "-3" ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
____________________________________
-3x / 3 = -1/-3 ;
____________________________________
to get: x = <span>⅓ .
_____________________________________
</span> → Now, let us check our answer by plugging in "<span>⅓" for all values of "x" in the ORIGINAL GIVEN EQUATION; to see if the equation holds true:
_____________________________________________________
</span> → 3x − 2 (x + 3) = 4x −<span> 7 ;
</span>→ [3 * (⅓) ] − 2 [ (⅓) + 3) = ? 4(⅓) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;
<span>
</span>→ (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;<span>
</span>→ (³/₃) − 2(¹⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ (³/₃) − (²⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;
→ ⁽³ ⁻²⁰⁾/₃) =? ⁽⁴⁻²¹⁾/₃) ??
→ ⁻¹⁷/₃ = ? ⁻¹⁷/₃ ?? Yes! Our answer "makes sense"!
_____________________________________________________
