Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-12}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & 1 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-28x & = &13\\\Leftrightarrow & \color{red}{-28}x & = &13\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{13}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{28} } & & \\ & V = \left\{ \frac{-13}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-9}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9-13x } & = & -6 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-9}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x } & = & -13 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-1}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-5x } & = & 15 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &9x & = &16\\\Leftrightarrow & \color{red}{9}x & = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+9}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x } & = & -5 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &24x & = &-14\\\Leftrightarrow & \color{red}{24}x & = &-14\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-14}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+12}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+2x } & = & -9 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &7x & = &-21\\\Leftrightarrow & \color{red}{7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-21}{7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+9}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-7x } & = & -8 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)