Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-15}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-11x } & = & 11 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &4x & = &26\\\Leftrightarrow & \color{red}{4}x & = &26\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{26}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-3}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-10x } & = & 13 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-8}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-13x } & = & -10 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+11}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+12x } & = & -15 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &25x & = &-26\\\Leftrightarrow & \color{red}{25}x & = &-26\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-26}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{25} } & & \\ & V = \left\{ \frac{-26}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-8}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & 15 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &23x & = &23\\\Leftrightarrow & \color{red}{23}x & = &23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{23}{23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-11}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-7x } & = & -5 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x } & = & 2 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &26x & = &-12\\\Leftrightarrow & \color{red}{26}x & = &-12\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-12}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+2}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-13x } & = & 4 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+7}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-5x } & = & -12 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-12}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+12x } & = & -3 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &25x & = &9\\\Leftrightarrow & \color{red}{25}x & = &9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)