Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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