Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-12}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & 2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-19x & = &14\\\Leftrightarrow & \color{red}{-19}x & = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & 5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+3}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-x } & = & -3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & -5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+7}& = & -6 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-2x } & = & -6 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-1}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-11x } & = & -3 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)