Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-8}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-13x } & = & 13 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+8}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-7x } & = & -11 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+2}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-4x } & = & 13 \color{red}{ +4x }\color{blue}{-2-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-3}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-5x } & = & 11 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-4}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-14x } & = & -13 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-25x & = &-9\\\Leftrightarrow & \color{red}{-25}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-11}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-11x } & = & 12 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-2x & = &23\\\Leftrightarrow & \color{red}{-2}x & = &23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-12}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -13 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-10}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-11x } & = & 3 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-19x & = &13\\\Leftrightarrow & \color{red}{-19}x & = &13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-1}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-7x } & = & -12 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-14}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14-7x } & = & -7 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-15}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-13x } & = & -1 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)