Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-5}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+11x } & = & -13 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+15}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-13x } & = & -10 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-25\\\Leftrightarrow & \color{red}{-19}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-25}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{25}{19} } & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-5}& = & -1 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+14x } & = & -1 \color{red}{ -14x }\color{blue}{+5+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-15}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x } & = & -6 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-18x & = &9\\\Leftrightarrow & \color{red}{-18}x & = &9\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{9}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+1}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-11x } & = & 12 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-10}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+11x } & = & -7 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-14}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-13x } & = & -3 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+10}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+3x } & = & 10 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-11}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+11x } & = & -10 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)