Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+15}& = &10 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-12}& = &-10 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+15}& = &-8 \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &-8x & = &-23\\\Leftrightarrow & \color{red}{-8}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-23}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+11}& = &6 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+7}& = &-6 \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = &4 \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+5}& = &1 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-13}& = &7 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+13}& = &6 \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13} & = &6\color{blue}{-13} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-15}& = &-8 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-2}& = &1 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &1\color{blue}{+2} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-8}& = &-2 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &-2\color{blue}{+8} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)