Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+12}& = &8 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &8\color{blue}{-12} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-6}& = &5 \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+5}& = &-8 \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+8}& = &7 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+4}& = &-15 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &4x & = &-19\\\Leftrightarrow & \color{red}{4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-5}& = &6 \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5} & = &6\color{blue}{+5} \\\Leftrightarrow &14x & = &11\\\Leftrightarrow & \color{red}{14}x & = &11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+13}& = &7 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-4}& = &4 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &4\color{blue}{+4} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+10}& = &-11 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-4x & = &-21\\\Leftrightarrow & \color{red}{-4}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{21}{4} } & & \\ & V = \left\{ \frac{21}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+10}& = &8 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &8\color{blue}{-10} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+3}& = &-12 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &-12\color{blue}{-3} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+15}& = &7 \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15} & = &7\color{blue}{-15} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)