Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-11}& = &-10 \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11} & = &-10\color{blue}{+11} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = &15 \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-8}& = &-8 \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+11}& = &-14 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &-x & = &-25\\\Leftrightarrow & \color{red}{-}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-25}{-1} \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+4}& = &15 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &15\color{blue}{-4} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+14}& = &-14 \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &-5x & = &-28\\\Leftrightarrow & \color{red}{-5}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-28}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{28}{5} } & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+7}& = &-7 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &-7\color{blue}{-7} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+3}& = &6 \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-7}& = &-7 \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+6}& = &-3 \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-3}& = &12 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-8}& = &12 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &9x & = &20\\\Leftrightarrow & \color{red}{9}x & = &20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)