Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-9}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-5x } & = & -15 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 1 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-4}& = & 5 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-14x } & = & 5 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+2}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-2x } & = & -10 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-24\\\Leftrightarrow & \color{red}{-12}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-24}{-12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+4}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+13x } & = & -13 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &27x & = &-17\\\Leftrightarrow & \color{red}{27}x & = &-17\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-17}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{27} } & & \\ & V = \left\{ \frac{-17}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-7}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-5x } & = & 8 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-x } & = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+13}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-4x } & = & -5 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)