Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+15}& = &-6 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &-6\color{blue}{-15} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-10}& = &3 \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10} & = &3\color{blue}{+10} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-13}& = &5 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &5\color{blue}{+13} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-8}& = &-15 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+14}& = &9 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &9\color{blue}{-14} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-15}& = &10 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+13}& = &-10 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13} & = &-10\color{blue}{-13} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-13}& = &7 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &12x & = &20\\\Leftrightarrow & \color{red}{12}x & = &20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-1}& = &-14 \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1} & = &-14\color{blue}{+1} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-11}& = &-13 \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11} & = &-13\color{blue}{+11} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-3}& = &-10 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-9}& = &10 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &4x & = &19\\\Leftrightarrow & \color{red}{4}x & = &19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)