Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-11}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-13x } & = & -12 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-25x & = &-1\\\Leftrightarrow & \color{red}{-25}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+4}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-11x } & = & -15 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-6}& = & -10 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+14x } & = & -10 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &14x & = &-15\\\Leftrightarrow & \color{red}{14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+3}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3+13x } & = & 13 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+2}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-8x } & = & 10 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-3}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+5x } & = & -7 \color{red}{ -5x }\color{blue}{+3+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)