Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 4 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-4}& = & -5 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-15x } & = & -5 \color{red}{ +15x }\color{blue}{+4-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+4}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-4x } & = & -12 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-16\\\Leftrightarrow & \color{red}{-19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & -2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+1}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+5x } & = & 12 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &18x & = &11\\\Leftrightarrow & \color{red}{18}x & = &11\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{11}{18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+8}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8-7x } & = & -9 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & -15 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4-11x } & = & -3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)