Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+15}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15+13x } & = & -3 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-12}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-14x } & = & -2 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-23x & = &10\\\Leftrightarrow & \color{red}{-23}x & = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-5}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+8x } & = & 1 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &17x & = &6\\\Leftrightarrow & \color{red}{17}x & = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+3}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-4x } & = & 7 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-10}& = & -12 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+10x } & = & -12 \color{red}{ -10x }\color{blue}{+10+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-12}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-3x } & = & -15 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+3}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-7x } & = & 15 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & 3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)