Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+5}& = &-3 \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5} & = &-3\color{blue}{-5} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-10}& = &11 \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+5}& = &-9 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &-9\color{blue}{-5} \\\Leftrightarrow &10x & = &-14\\\Leftrightarrow & \color{red}{10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+9}& = &6 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &6\color{blue}{-9} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-7}& = &5 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+13}& = &-3 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-4}& = &12 \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+2}& = &8 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &8\color{blue}{-2} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+13}& = &-2 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-14}& = &4 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+13}& = &-13 \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13} & = &-13\color{blue}{-13} \\\Leftrightarrow &14x & = &-26\\\Leftrightarrow & \color{red}{14}x & = &-26\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-26}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = &-8 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)