Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-8}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-11x } & = & -14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-18x & = &-6\\\Leftrightarrow & \color{red}{-18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-1}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+10x } & = & -3 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-6}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+11x } & = & -2 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &25x & = &4\\\Leftrightarrow & \color{red}{25}x & = &4\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{4}{25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+15}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15-12x } & = & 13 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+8}& = & -9 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8-15x } & = & -9 \color{red}{ +15x }\color{blue}{-8-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-9x & = &26\\\Leftrightarrow & \color{red}{-9}x & = &26\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{26}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-6}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-11x } & = & 14 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-11}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-12x } & = & -11 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-2}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-13x } & = & -1 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)