Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+9}& = &-10 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &9x & = &-19\\\Leftrightarrow & \color{red}{9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-3}& = &-2 \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3} & = &-2\color{blue}{+3} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+1}& = &-10 \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1} & = &-10\color{blue}{-1} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+4}& = &6 \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4} & = &6\color{blue}{-4} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+2}& = &11 \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+2}& = &-8 \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2} & = &-8\color{blue}{-2} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+15}& = &10 \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+10}& = &-15 \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10} & = &-15\color{blue}{-10} \\\Leftrightarrow &11x & = &-25\\\Leftrightarrow & \color{red}{11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-6}& = &-12 \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6} & = &-12\color{blue}{+6} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-8}& = &15 \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &-10x & = &23\\\Leftrightarrow & \color{red}{-10}x & = &23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{10} } & & \\ & V = \left\{ \frac{-23}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-4}& = &11 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &11\color{blue}{+4} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-15}& = &-15 \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)