Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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