Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+1}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+6x } & = & -1 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & 1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-12}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12+10x } & = & 3 \color{red}{ -10x }\color{blue}{+12+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-22\\\Leftrightarrow & \color{red}{-11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-22}{-11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+10}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-8x } & = & -9 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-21x & = &-19\\\Leftrightarrow & \color{red}{-21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+10}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10+2x } & = & -13 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &9x & = &-23\\\Leftrightarrow & \color{red}{9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-5}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -1 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+14}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-13x } & = & 12 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)