Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+2}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+10x } & = & 4 \color{red}{ -10x }\color{blue}{-2+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-7}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-14x } & = & 10 \color{red}{ +14x }\color{blue}{+7-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-25x & = &17\\\Leftrightarrow & \color{red}{-25}x & = &17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{25} } & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+2}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-x } & = & -8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+6}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-13x } & = & -13 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-15}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+13x } & = & -9 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &24x & = &6\\\Leftrightarrow & \color{red}{24}x & = &6\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{6}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & 10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & -15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+2}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2+5x } & = & 13 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+3}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-10x } & = & -8 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-19x & = &-11\\\Leftrightarrow & \color{red}{-19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)