Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+14}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-11x } & = & 9 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-6}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 5 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-1}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1+2x } & = & -7 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-2}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+3x } & = & 2 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 2 \color{blue}{+2} \\\Leftrightarrow &16x & = &4\\\Leftrightarrow & \color{red}{16}x & = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+15}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-13x } & = & -9 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-28x & = &-24\\\Leftrightarrow & \color{red}{-28}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+13}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-5x } & = & -8 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+9}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-7x } & = & -8 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-9}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9+11x } & = & -7 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)