Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+6}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+3x } & = & -5 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+3}& = & -14 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-12x } & = & -14 \color{red}{ +12x }\color{blue}{-3-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-19x & = &-17\\\Leftrightarrow & \color{red}{-19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-17}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-13}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & 2 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & -15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+6}& = & -1 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+10x } & = & -1 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-2}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-7x } & = & -8 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-8}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & -9 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-6}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-5x } & = & 10 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & 15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)