Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+8}& = &-9 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &-9\color{blue}{-8} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-14}& = &-5 \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+11}& = &12 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &12\color{blue}{-11} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-15}& = &-1 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &-1\color{blue}{+15} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+6}& = &-6 \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+14}& = &-4 \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+11}& = &-8 \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-3}& = &13 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &13\color{blue}{+3} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-10}& = &-11 \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10} & = &-11\color{blue}{+10} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-7}& = &-14 \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7} & = &-14\color{blue}{+7} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+15}& = &10 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-5}& = &-6 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &-6\color{blue}{+5} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)