Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+9}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-8x } & = & 10 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+9}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+5x } & = & -12 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-12}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-4x } & = & -5 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+11}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 3 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &23x & = &-8\\\Leftrightarrow & \color{red}{23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+4}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+14x } & = & -7 \color{red}{ -14x }\color{blue}{-4+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &15x & = &-11\\\Leftrightarrow & \color{red}{15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-15}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-13x } & = & -12 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+5}& = & 5 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+12x } & = & 5 \color{red}{ -12x }\color{blue}{-5+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &25x & = &0\\\Leftrightarrow & \color{red}{25}x & = &0\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{0}{25} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &14x & = &-25\\\Leftrightarrow & \color{red}{14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-7x } & = & -11 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)