Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-9}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-7x } & = & 1 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-x } & = & 11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & 8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-12}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-9x } & = & -9 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+8}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+6x } & = & 11 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &19x & = &3\\\Leftrightarrow & \color{red}{19}x & = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-1}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+13x } & = & 4 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &21x & = &5\\\Leftrightarrow & \color{red}{21}x & = &5\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{5}{21} \\\Leftrightarrow & \color{green}{ x = \frac{5}{21} } & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+3}& = & 7 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+14x } & = & 7 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+5}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-13x } & = & 9 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-5}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+7x } & = & 2 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)