Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-2}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-13x } & = & -5 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-12}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+13x } & = & -8 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &12x & = &4\\\Leftrightarrow & \color{red}{12}x & = &4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-7}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+8x } & = & 13 \color{red}{ -8x }\color{blue}{+7+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x } & = & 10 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+3}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3+13x } & = & 3 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+14}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+7x } & = & -10 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &6x & = &-24\\\Leftrightarrow & \color{red}{6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-24}{6} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+13}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-9x } & = & 5 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+2}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-2x } & = & -5 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)