Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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