Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-10}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-5x } & = & 3 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-7}& = & 7 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+14x } & = & 7 \color{red}{ -14x }\color{blue}{+7+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+2}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-5x } & = & -4 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-10}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10+9x } & = & -13 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+4}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+3x } & = & 13 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &10x & = &9\\\Leftrightarrow & \color{red}{10}x & = &9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+6}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-8x } & = & 3 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+14}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x } & = & 11 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &26x & = &-3\\\Leftrightarrow & \color{red}{26}x & = &-3\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-3}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{26} } & & \\ & V = \left\{ \frac{-3}{26} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-5}& = & 1 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+10x } & = & 1 \color{red}{ -10x }\color{blue}{+5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-11}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+5x } & = & -9 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &18x & = &2\\\Leftrightarrow & \color{red}{18}x & = &2\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{2}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)