Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-7x } & = & 14 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+6}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-3x } & = & -1 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-3}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-5x } & = & 10 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+2x } & = & 4 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &9x & = &10\\\Leftrightarrow & \color{red}{9}x & = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-14}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+11x } & = & 12 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &17x & = &26\\\Leftrightarrow & \color{red}{17}x & = &26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-4}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+5x } & = & 6 \color{red}{ -5x }\color{blue}{+4+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &6x & = &10\\\Leftrightarrow & \color{red}{6}x & = &10\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{10}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -9 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-23\\\Leftrightarrow & \color{red}{-11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & 4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)