Answer:
2.(b) w= 3
3. x= -3 or x= 3
Step-by-step explanation:
2.(b) Method 1:
[tex] \frac{2w - 1}{5} + w + 2 = 2w \\ \frac{2w - 1}{5} = 2w - w - 2 \\ [/tex]
Simplify:
[tex] \frac{2w - 1}{5} = w - 2[/tex]
×5 on both sides:
[tex]2w - 1 = 5(w - 2)[/tex]
Expand:
[tex]2w - 1 = 5w - 10[/tex]
Bring constants to 1 side, w terms to the other:
[tex]5w - 2w = 10 - 1[/tex]
Simplify:
[tex]3w = 9[/tex]
Divide both sides by 3:
[tex]w = 9 \div 3 \\ w = 3[/tex]
Method 2:
[tex] \frac{2w - 1}{5} + w + 2 = 2w[/tex]
Multiply by 5 throughout:
[tex]2w - 1 + 5(w + 2) = 5(2w)[/tex]
Expand:
[tex]2w - 1 + 5w + 10 = 4w[/tex]
Simplify:
[tex]7w - 9 = 4w[/tex]
+9 on both sides:
[tex]7w = 4w + 9[/tex]
-4w on both sides:
[tex]7w - 4w = 9[/tex]
Simplify:
[tex]3w = 9[/tex]
Divide by 3 on both sides:
[tex]w = 3[/tex]
3. [tex] \frac{6x - 12}{3} + 4 = \frac{18}{x} [/tex]
Multiply by 3x on both sides:
[tex] \frac{3x(6x - 12)}{3} + 3x(4) = \frac{3x(18)}{x} \\ x(6x - 12) + 12x = 3(18)[/tex]
Expand:
[tex]x(6x) - x(12) + 12x = 54 \\ 6x^{2} - 12x + 12x = 54 \\[/tex]
Simplify:
[tex]6 {x}^{2} = 54[/tex]
Divide by 6 on both sides:
[tex] {x}^{2} = 9[/tex]
-9 on both sides:
[tex] {x}^{2} - 9 = 0[/tex]
Factorise:
*Since a²-b²= (a +b)(a -b),
[tex] {x}^{2} - {3}^{2} = 0 \\ (x + 3)(x - 3) = 0[/tex]
Thus,
x +3= 0 or x -3= 0
x= -3 or x= 3
