Linear(Simple) Equations: Very Difficult Problems with Solutions

Solution:
The statement is equivalent to the following equation:
[tex]x=7x-18[/tex]
[tex]18=7x-x[/tex]
[tex]6x=18[/tex]
[tex]x=3[/tex]

Solution:
Let us denote the number with n. The problem can be rewritten as n=4n-75. By substracting n from both sides, we get 3n-75=0. Now we divide both sides by 3 to get n-25=0, or n=25.

Solution:
Let us denote the number with n. We rewrite the problem as 2n-12=3n-15. We substract 2n from both sides and get -12=n-15. Then we add 15 to both sides in order to get n=3.

Solution:
[tex]2x=5x+18[/tex]
[tex]3x=-18[/tex]
[tex]x=-6[/tex]

Solution:
(a + b) + (b + c) + (a + c) = 29 + 45 + 44
a + b + b + c + a + c = 118
2a + 2b + 2c = 118
2(a + b + c) = 118
a + b + c = 59

Solution:
Answer: x = -5

Solution:
[tex]x- \frac{1-\frac{3x}{2}}{4} = \frac{2-\frac{x}{4}}{3} - \frac{11}{12}[/tex]

Multiply the both sides by 12 and we get:

[tex]12x- 12\frac{1-\frac{3x}{2}}{4} = 12\frac{2-\frac{x}{4}}{3} - 12\frac{11}{12}[/tex]

[tex]12x- 3(1-\frac{3x}{2}) = 4(2-\frac{x}{4}) - 11[/tex]

[tex]12x- 3+\frac{9x}{2} = 8-\frac{4x}{4} - 11[/tex]

[tex]12x- 3+\frac{9x}{2} = -x - 3[/tex]

[tex]12x+\frac{9x}{2} = -x[/tex]

[tex]13x+\frac{9x}{2} = 0[/tex]

Multiply by 2

[tex]26x+9x = 0[/tex]

[tex]35x = 0[/tex]

[tex]x = 0[/tex]