Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+5}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-5x } & = & -4 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-8}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-13x } & = & -15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-12}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-13x } & = & 14 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-7x & = &26\\\Leftrightarrow & \color{red}{-7}x & = &26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-14}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+13x } & = & -15 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-3}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+2x } & = & -9 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+7}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-4x } & = & -3 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-12}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & -14 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-19x & = &-2\\\Leftrightarrow & \color{red}{-19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+6}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-11x } & = & 14 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-21x & = &8\\\Leftrightarrow & \color{red}{-21}x & = &8\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{8}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+9}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-9x } & = & 5 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)