Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-1}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+6x } & = & -14 \color{red}{ -6x }\color{blue}{+1+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & -15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+9}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-13x } & = & -5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-14\\\Leftrightarrow & \color{red}{-17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-5}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-4x } & = & 15 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-6}& = & -14 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x } & = & -14 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-15}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-10x } & = & 10 \color{red}{ +10x }\color{blue}{+15-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-4}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-2x } & = & -10 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+6}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-3x } & = & -8 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)