Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+1}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+4x } & = & -3 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &6x & = &4\\\Leftrightarrow & \color{red}{6}x & = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+1}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-5x } & = & -8 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-9x } & = & 3 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-10}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-11x } & = & -14 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-10}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+8x } & = & -13 \color{red}{ -8x }\color{blue}{+10+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-5}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-9x } & = & 13 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-20x & = &18\\\Leftrightarrow & \color{red}{-20}x & = &18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+5}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-5x } & = & -15 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-2}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+4x } & = & -7 \color{red}{ -4x }\color{blue}{+2+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)