Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+11}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+7x } & = & 4 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &12x & = &-7\\\Leftrightarrow & \color{red}{12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+3}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-4x } & = & -3 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+5}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-10x } & = & 9 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+11}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-9x } & = & 4 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+6}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+9x } & = & 1 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &16x & = &-5\\\Leftrightarrow & \color{red}{16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-5}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-5}& = & -15 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-15x } & = & -15 \color{red}{ +15x }\color{blue}{+5-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-1}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-14x } & = & 7 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-4}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-7x } & = & 14 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &-16x & = &18\\\Leftrightarrow & \color{red}{-16}x & = &18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+14}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-5x } & = & 12 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+6}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+2x } & = & 2 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)