Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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