Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+13}& = &9 \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-1}& = &5 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-7}& = &-7 \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+1}& = &15 \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1} & = &15\color{blue}{-1} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-10}& = &8 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &8\color{blue}{+10} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+2}& = &11 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-15}& = &-8 \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+1}& = &9 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &9\color{blue}{-1} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+10}& = &-1 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-1}& = &5 \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-4}& = &10 \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+10}& = &11 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &11\color{blue}{-10} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)