Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-7}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-7x } & = & 4 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-8}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-7x } & = & 9 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+12}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-11x } & = & -12 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+12}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12-11x } & = & 14 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & -15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-12}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+9x } & = & -4 \color{red}{ -9x }\color{blue}{+12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &14x & = &8\\\Leftrightarrow & \color{red}{14}x & = &8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-14}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-13x } & = & 7 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-2x & = &21\\\Leftrightarrow & \color{red}{-2}x & = &21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-4}& = & -11 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-15x } & = & -11 \color{red}{ +15x }\color{blue}{+4-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-13}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-14x } & = & -15 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)