Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(11x-8=-11+5x\)
2. \(14x+4=13+9x\)
3. \(-7x+9=10+x\)
4. \(-12x+3=-10+13x\)
5. \(-3x+15=-12+10x\)
6. \(-x-5=7+0x\)
7. \(-x-1=8-5x\)
8. \(7x-10=-6-9x\)
9. \(-7x-15=14+8x\)
10. \(-5x-2=12+6x\)
11. \(x-8=9+8x\)
12. \(8x+7=3+11x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-8}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8-5x } & = & -11 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+4}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-9x } & = & 13 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+3}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x } & = & -10 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-25x & = &-13\\\Leftrightarrow & \color{red}{-25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+15}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-10x } & = & -12 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-27\\\Leftrightarrow & \color{red}{-13}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-27}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{27}{13} } & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-5}& = & 7 \color{red}{ +0x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+0x } & = & 7 \color{red}{ +0x }\color{blue}{+5+0x } \\\Leftrightarrow & -x \color{blue}{+0x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+5x } & = & 8 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-10}& = & -6 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+9x } & = & -6 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &16x & = &4\\\Leftrightarrow & \color{red}{16}x & = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-15}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-8x } & = & 14 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-15x & = &29\\\Leftrightarrow & \color{red}{-15}x & = &29\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{29}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{15} } & & \\ & V = \left\{ \frac{-29}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-2}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-6x } & = & 12 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-8}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-8x } & = & 9 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+7}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-11x } & = & 3 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)