Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-4}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4+13x } & = & -5 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &24x & = &-1\\\Leftrightarrow & \color{red}{24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+12}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x } & = & -11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+12}& = & 12 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+12x } & = & 12 \color{red}{ -12x }\color{blue}{-12+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-15}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & -13 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+13}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+11x } & = & 12 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+6}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6-11x } & = & 14 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-15}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-13x } & = & -7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+13}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & 6 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-9}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+12x } & = & 6 \color{red}{ -12x }\color{blue}{+9+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &25x & = &15\\\Leftrightarrow & \color{red}{25}x & = &15\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{15}{25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)