Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-2}& = & -7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -7 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+7}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-13x } & = & -12 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-25x & = &-19\\\Leftrightarrow & \color{red}{-25}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{19}{25} } & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+8}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+6x } & = & -9 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+9}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-5x } & = & -12 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-2}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-7x } & = & -9 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-9}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-14x } & = & 15 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-25x & = &24\\\Leftrightarrow & \color{red}{-25}x & = &24\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{24}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{25} } & & \\ & V = \left\{ \frac{-24}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-8}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+5x } & = & 2 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)