Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+7}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+7x } & = & 2 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &22x & = &-5\\\Leftrightarrow & \color{red}{22}x & = &-5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{22} } & & \\ & V = \left\{ \frac{-5}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+11}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+13x } & = & -8 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &21x & = &-19\\\Leftrightarrow & \color{red}{21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{21} } & & \\ & V = \left\{ \frac{-19}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+15}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+8x } & = & -6 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+4}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-7x } & = & -15 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &6x & = &-19\\\Leftrightarrow & \color{red}{6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-19}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+8}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-13x } & = & -12 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-16x & = &23\\\Leftrightarrow & \color{red}{-16}x & = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+1}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-7x } & = & 3 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)