Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-x } & = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+7}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-11x } & = & -2 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-2}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2+13x } & = & 6 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &27x & = &8\\\Leftrightarrow & \color{red}{27}x & = &8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+10}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-9x } & = & 9 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & -12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-6x & = &23\\\Leftrightarrow & \color{red}{-6}x & = &23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+1}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-3x } & = & 7 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-13}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-7x } & = & 9 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+3}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-4x } & = & -3 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-14}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-11x } & = & 5 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)