Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-3}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-13x } & = & 1 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-8}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+5x } & = & -5 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &16x & = &3\\\Leftrightarrow & \color{red}{16}x & = &3\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{3}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+7}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+4x } & = & -2 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+13}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & -12 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &19x & = &-25\\\Leftrightarrow & \color{red}{19}x & = &-25\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-25}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{19} } & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+15}& = & 13 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15-2x } & = & 13 \color{red}{ +2x }\color{blue}{-15-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+7}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-14x } & = & 1 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-6\\\Leftrightarrow & \color{red}{-25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+6x } & = & -4 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-10}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10+11x } & = & -1 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)