Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-13x } & = & -7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-14}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-9x } & = & 6 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-13}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-11x } & = & 5 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & 4 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+11}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-11x } & = & -1 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+6}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-9x } & = & 6 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)