Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-9}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-12x } & = & -11 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-3}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & 13 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &27x & = &16\\\Leftrightarrow & \color{red}{27}x & = &16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{16}{27} } & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-8}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+10x } & = & 4 \color{red}{ -10x }\color{blue}{+8+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &21x & = &12\\\Leftrightarrow & \color{red}{21}x & = &12\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{12}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+1}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-13x } & = & 3 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-3}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & -3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+4}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+13x } & = & 10 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &22x & = &6\\\Leftrightarrow & \color{red}{22}x & = &6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+4}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-11x } & = & 2 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)