Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & -11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-23\\\Leftrightarrow & \color{red}{-16}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{23}{16} } & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-10x & = &22\\\Leftrightarrow & \color{red}{-10}x & = &22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &14x & = &9\\\Leftrightarrow & \color{red}{14}x & = &9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+6}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-14x } & = & -6 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+13}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-13x } & = & 2 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & -8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+7}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-5x } & = & -1 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)