Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+3}& = &14 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-7}& = &-13 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-3}& = &-3 \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3} & = &-3\color{blue}{+3} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-12}& = &15 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &12x & = &27\\\Leftrightarrow & \color{red}{12}x & = &27\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{27}{12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+15}& = &15 \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-15}& = &9 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &9\color{blue}{+15} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+9}& = &14 \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9} & = &14\color{blue}{-9} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-15}& = &-10 \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15} & = &-10\color{blue}{+15} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+1}& = &5 \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1} & = &5\color{blue}{-1} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-7}& = &2 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &2\color{blue}{+7} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-3}& = &6 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+3}& = &9 \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)