Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-5}& = & -10 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-15x } & = & -10 \color{red}{ +15x }\color{blue}{+5-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+5}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+4x } & = & 12 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-x } & = & 8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-15}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-11x } & = & 3 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+12}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+13x } & = & 9 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &24x & = &-3\\\Leftrightarrow & \color{red}{24}x & = &-3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+3}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+6x } & = & 1 \color{red}{ -6x }\color{blue}{-3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-15}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+13x } & = & 13 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &23x & = &28\\\Leftrightarrow & \color{red}{23}x & = &28\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{28}{23} \\\Leftrightarrow & \color{green}{ x = \frac{28}{23} } & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-8}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-5x } & = & 8 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)