Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+2}& = & -15 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+9x } & = & -15 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -15 \color{blue}{-2} \\\Leftrightarrow &14x & = &-17\\\Leftrightarrow & \color{red}{14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+11}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-7x } & = & -12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-23\\\Leftrightarrow & \color{red}{-17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{23}{17} } & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -3 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+6}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-14x } & = & -14 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-11}& = & 4 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-10x } & = & 4 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-19x & = &15\\\Leftrightarrow & \color{red}{-19}x & = &15\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{15}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{19} } & & \\ & V = \left\{ \frac{-15}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-2x & = &-20\\\Leftrightarrow & \color{red}{-2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-20}{-2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-14}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-x } & = & -15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-13}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+11x } & = & -10 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -10 \color{blue}{+13} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)