Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+7}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+3x } & = & 2 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-x } & = & 3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-6}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+3x } & = & 7 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-7}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-8x } & = & -4 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-14}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-7x } & = & 9 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-13x & = &23\\\Leftrightarrow & \color{red}{-13}x & = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-11}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-11x } & = & -13 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-21x & = &-2\\\Leftrightarrow & \color{red}{-21}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-2}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{21} } & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-9}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-11x } & = & 5 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-4}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-11x } & = & 15 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-16x & = &19\\\Leftrightarrow & \color{red}{-16}x & = &19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-1}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-12x } & = & -1 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)