Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+5}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+7x } & = & -15 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+4}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+4x } & = & -9 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+8}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x } & = & -11 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-19\\\Leftrightarrow & \color{red}{-19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-19}{-19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+8}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-8x } & = & -15 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-23\\\Leftrightarrow & \color{red}{-3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-1}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 4 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-6}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & 14 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+15}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-3x } & = & 2 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)