Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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