Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-x } & = & 9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+5}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5+11x } & = & 15 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &25x & = &10\\\Leftrightarrow & \color{red}{25}x & = &10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-4}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-13x } & = & -2 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+6}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-5x } & = & 8 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-1}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-5x } & = & -9 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-10}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+3x } & = & 7 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+8}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-7x } & = & -6 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+9x } & = & 9 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-6}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+12x } & = & 6 \color{red}{ -12x }\color{blue}{+6+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)