Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+2}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2+3x } & = & -4 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &16x & = &-6\\\Leftrightarrow & \color{red}{16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-6}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & 14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+14}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-8x } & = & 8 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-15}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-7x } & = & 11 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-10x & = &26\\\Leftrightarrow & \color{red}{-10}x & = &26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-5}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+15x } & = & -6 \color{red}{ -15x }\color{blue}{+5+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-5}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & 9 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-11}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+3x } & = & -7 \color{red}{ -3x }\color{blue}{+11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)