Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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