Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-6}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-13x } & = & -9 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+10}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-6x } & = & 6 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+10}& = & 14 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+14x } & = & 14 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-3x } & = & -12 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-8}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+8x } & = & -15 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+11}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-14x } & = & 14 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-15}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-9x } & = & 14 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-13x & = &29\\\Leftrightarrow & \color{red}{-13}x & = &29\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{29}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{13} } & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-14}& = & 9 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-6x } & = & 9 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)