Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+10}& = &-7 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+1}& = &-14 \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1} & = &-14\color{blue}{-1} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+12}& = &9 \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-10}& = &-8 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &-8\color{blue}{+10} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-13}& = &-12 \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13} & = &-12\color{blue}{+13} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+2}& = &1 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &1\color{blue}{-2} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-14}& = &4 \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+11}& = &-14 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+6}& = &13 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &13\color{blue}{-6} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-12}& = &-7 \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-9}& = &-3 \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9} & = &-3\color{blue}{+9} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+8}& = &5 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &5\color{blue}{-8} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)