Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-13}& = &12 \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &-10x & = &25\\\Leftrightarrow & \color{red}{-10}x & = &25\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{25}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+14}& = &-2 \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-14}& = &6 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &6\color{blue}{+14} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+1}& = &-15 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+3}& = &6 \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-9}& = &5 \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-4}& = &7 \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4} & = &7\color{blue}{+4} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+11}& = &-3 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &-3\color{blue}{-11} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-14}& = &5 \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14} & = &5\color{blue}{+14} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+1}& = &12 \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1} & = &12\color{blue}{-1} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-12}& = &-12 \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-6}& = &-2 \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6} & = &-2\color{blue}{+6} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)