Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+4}& = &5 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+12}& = &12 \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-4}& = &10 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-4}& = &-12 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+3}& = &11 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &11\color{blue}{-3} \\\Leftrightarrow &8x & = &8\\\Leftrightarrow & \color{red}{8}x & = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-14}& = &13 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &3x & = &27\\\Leftrightarrow & \color{red}{3}x & = &27\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{27}{3} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-15}& = &6 \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+13}& = &14 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-7}& = &11 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &11\color{blue}{+7} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-3}& = &-4 \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-10}& = &6 \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10} & = &6\color{blue}{+10} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-8}& = &4 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &4\color{blue}{+8} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)