Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+5}& = &-10 \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5} & = &-10\color{blue}{-5} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+9}& = &6 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &6\color{blue}{-9} \\\Leftrightarrow &14x & = &-3\\\Leftrightarrow & \color{red}{14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+6}& = &4 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+9}& = &-15 \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9} & = &-15\color{blue}{-9} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-3}& = &9 \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3} & = &9\color{blue}{+3} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+15}& = &-8 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &10x & = &-23\\\Leftrightarrow & \color{red}{10}x & = &-23\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-23}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{10} } & & \\ & V = \left\{ \frac{-23}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+11}& = &9 \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11} & = &9\color{blue}{-11} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+1}& = &9 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &9\color{blue}{-1} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-11}& = &-5 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-13}& = &10 \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-3}& = &-6 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &-6\color{blue}{+3} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+15}& = &11 \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15} & = &11\color{blue}{-15} \\\Leftrightarrow &-2x & = &-4\\\Leftrightarrow & \color{red}{-2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-4}{-2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)