Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-15}& = &-11 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+6}& = &10 \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6} & = &10\color{blue}{-6} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-6}& = &-2 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &-2\color{blue}{+6} \\\Leftrightarrow &6x & = &4\\\Leftrightarrow & \color{red}{6}x & = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+2}& = &-14 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &-14\color{blue}{-2} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-6}& = &6 \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6} & = &6\color{blue}{+6} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+3}& = &-4 \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3} & = &-4\color{blue}{-3} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-11}& = &-2 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+5}& = &3 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+5}& = &15 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &15\color{blue}{-5} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-11}& = &12 \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &4x & = &23\\\Leftrightarrow & \color{red}{4}x & = &23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-7}& = &9 \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7} & = &9\color{blue}{+7} \\\Leftrightarrow &15x & = &16\\\Leftrightarrow & \color{red}{15}x & = &16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+15}& = &10 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)