Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-6}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+15x } & = & 4 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+10}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+7x } & = & -4 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-13}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-11x } & = & -9 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+6}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+7x } & = & 2 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &22x & = &-4\\\Leftrightarrow & \color{red}{22}x & = &-4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-7}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-11x } & = & 7 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-24x & = &14\\\Leftrightarrow & \color{red}{-24}x & = &14\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{14}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-3}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-5x } & = & 5 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+8}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x } & = & 5 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & -13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-28\\\Leftrightarrow & \color{red}{-15}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)