Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+12}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-6x } & = & 2 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-7}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+13x } & = & -6 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &27x & = &1\\\Leftrightarrow & \color{red}{27}x & = &1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-8}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-10x } & = & -4 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-8}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-10x } & = & -12 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+7}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-7x } & = & 7 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-4}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-13x } & = & -5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-28x & = &-1\\\Leftrightarrow & \color{red}{-28}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{28} } & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-15}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-5x } & = & -8 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-11}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-13x } & = & -9 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-5x } & = & -14 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-13\\\Leftrightarrow & \color{red}{-19}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)