Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-9}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-7x } & = & 14 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+2}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-8x } & = & -6 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & -3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+7}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+11x } & = & -11 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &25x & = &-18\\\Leftrightarrow & \color{red}{25}x & = &-18\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-18}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{25} } & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-2}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+8x } & = & 14 \color{red}{ -8x }\color{blue}{+2+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+5}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-13x } & = & 4 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+13}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-8x } & = & 9 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)