Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+14}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-3x } & = & -2 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &x & = &-16\\\Leftrightarrow & \color{red}{}x & = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-4}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-5x } & = & 3 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-12x & = &29\\\Leftrightarrow & \color{red}{-12}x & = &29\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{29}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{12} } & & \\ & V = \left\{ \frac{-29}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-3}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & -7 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &25x & = &-4\\\Leftrightarrow & \color{red}{25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &6x & = &17\\\Leftrightarrow & \color{red}{6}x & = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+9}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+11x } & = & -6 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-1}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-3x } & = & -4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-11}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-9x } & = & 14 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-20x & = &25\\\Leftrightarrow & \color{red}{-20}x & = &25\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{25}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+14}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+9x } & = & -15 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &8x & = &-29\\\Leftrightarrow & \color{red}{8}x & = &-29\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-29}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{8} } & & \\ & V = \left\{ \frac{-29}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)