Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(-12x+7=2+x\)
2. \(-3x+15=7+x\)
3. \(15x-10=-12-7x\)
4. \(x+13=2+0x\)
5. \(7x-8=-9-13x\)
6. \(6x+11=-2+7x\)
7. \(10x-8=8-9x\)
8. \(-10x-7=-1+x\)
9. \(-3x-14=10+x\)
10. \(10x-1=-4-13x\)
11. \(9x+12=5+13x\)
12. \(-9x-7=11+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & 2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-10}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+7x } & = & -12 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &22x & = &-2\\\Leftrightarrow & \color{red}{22}x & = &-2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+13}& = & 2 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13+0x } & = & 2 \color{red}{ +0x }\color{blue}{-13+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-8}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+13x } & = & -9 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &20x & = &-1\\\Leftrightarrow & \color{red}{20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-1}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+11}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-7x } & = & -2 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-8}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+9x } & = & 8 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -1 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-1}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1+13x } & = & -4 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+12}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-13x } & = & 5 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & 11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)