Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-2}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-11x } & = & 14 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &4x & = &16\\\Leftrightarrow & \color{red}{4}x & = &16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{16}{4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+9}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-14x } & = & 2 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+13}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-7x } & = & -1 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+15}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15-13x } & = & 4 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & 2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+5}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5+13x } & = & 14 \color{red}{ -13x }\color{blue}{-5+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &12x & = &9\\\Leftrightarrow & \color{red}{12}x & = &9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-4}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-5x } & = & -14 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-15}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15+7x } & = & 14 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &15x & = &29\\\Leftrightarrow & \color{red}{15}x & = &29\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{29}{15} \\\Leftrightarrow & \color{green}{ x = \frac{29}{15} } & & \\ & V = \left\{ \frac{29}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+9}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-4x } & = & 11 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)