Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-4}& = &9 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+8}& = &-4 \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8} & = &-4\color{blue}{-8} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-10}& = &-15 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-2}& = &-1 \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+5}& = &-4 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &-4\color{blue}{-5} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+14}& = &8 \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14} & = &8\color{blue}{-14} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+10}& = &-7 \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-12}& = &11 \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-14}& = &-10 \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14} & = &-10\color{blue}{+14} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+15}& = &-6 \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15} & = &-6\color{blue}{-15} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+8}& = &10 \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+9}& = &12 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)