Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+4}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4-11x } & = & -1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-6}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+9x } & = & 11 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &19x & = &17\\\Leftrightarrow & \color{red}{19}x & = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+1}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-10x } & = & -6 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-x } & = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-5}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & 8 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-17x & = &13\\\Leftrightarrow & \color{red}{-17}x & = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+7}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+13x } & = & -14 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &20x & = &-21\\\Leftrightarrow & \color{red}{20}x & = &-21\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-21}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{20} } & & \\ & V = \left\{ \frac{-21}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+6}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-4x } & = & -1 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+13}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+13x } & = & -7 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &22x & = &-20\\\Leftrightarrow & \color{red}{22}x & = &-20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+1}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-13x } & = & 12 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-18x & = &11\\\Leftrightarrow & \color{red}{-18}x & = &11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{18} } & & \\ & V = \left\{ \frac{-11}{18} \right\} & \\\end{align}\)