[tex] \div\: a,b,c < = > b = \frac{a + c}{2} [/tex]
[tex]e)a = x + 4[/tex]
[tex]b = 2x + 5[/tex]
[tex]c = x + 8[/tex]
[tex]b = \frac{a + c}{2} [/tex]
[tex]2x + 5 = \frac{x + 4 + x + 8}{2} [/tex]
[tex]2x + 5 = \frac{2x + 12}{2} [/tex]
[tex]2x + 5 = \frac{2(x + 6)}{2} [/tex]
[tex]2x + 5 = x + 6[/tex]
[tex]2x - x = 6 - 5[/tex]
[tex]x = 1[/tex]
[tex]f)a = x + 1[/tex]
[tex]b = 3x[/tex]
[tex]c = 2x + 5[/tex]
[tex]b = \frac{a + c}{2} [/tex]
[tex]3x = \frac{ x + 1 + 2x + 5 }{2} [/tex]
[tex]3x = \frac{3x + 6}{2} [/tex]
[tex]3x \times 2= 3x + 6[/tex]
[tex]6x = 3x + 6[/tex]
[tex]6x - 3x = 6[/tex]
[tex]3x = 6 \: | \div 3[/tex]
[tex]x = 2[/tex]
[tex]g)a = {x}^{2} - 1[/tex]
[tex]b = 3x - 4[/tex]
[tex]c = x - 1[/tex]
[tex]b = \frac{a + c}{2} [/tex]
[tex]3x - 4 = \frac{ {x}^{2} - 1 + x - 1 }{2} [/tex]
[tex]3x - 4 = \frac{ {x}^{2} + x - 2 }{2} [/tex]
[tex]2(3x - 4) = {x}^{2} + x - 2[/tex]
[tex]6x - 8 = {x}^{2} + x - 2[/tex]
[tex] - {x}^{2} + 6x - x - 8 + 2 = 0[/tex]
[tex] - {x}^{2} + 5x - 6 = 0 \: | \times ( - 1)[/tex]
[tex] {x}^{2} - 5x + 6 = 0[/tex]
[tex] {x}^{2} - 2x - 3x + 6 = 0[/tex]
[tex]x(x - 2) - 3(x - 2) = 0[/tex]
[tex](x - 3)(x - 2) = 0[/tex]
[tex]x - 3 = 0 = > x = 3[/tex]
[tex]x - 2 = 0 = > x = 2[/tex]
[tex]h)a = x - 2[/tex]
[tex]b = {x}^{2} [/tex]
[tex]c = x + 6[/tex]
[tex]b = \frac{a + c}{2} [/tex]
[tex] {x}^{2} = \frac{x - 2 + x + 6}{2} [/tex]
[tex] {x}^{2} = \frac{2x + 4}{2} [/tex]
[tex] {x}^{2} = \frac{2(x + 2)}{2} [/tex]
[tex] {x}^{2} = x + 2[/tex]
[tex] {x}^{2} - x - 2 = 0[/tex]
[tex] {x}^{2} - 2x + x - 2 = 0[/tex]
[tex]x(x - 2) +1( x - 2 )= 0[/tex]
[tex](x - 2)(x + 1) = 0[/tex]
[tex]x - 2 = 0 = > x = 2[/tex]
[tex]x + 1 = 0 = > x = - 1[/tex]
