Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+7}& = &12 \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7} & = &12\color{blue}{-7} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+4}& = &9 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &9\color{blue}{-4} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-6}& = &-14 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+10}& = &13 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &13\color{blue}{-10} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-9}& = &7 \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+14}& = &15 \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+4}& = &15 \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4} & = &15\color{blue}{-4} \\\Leftrightarrow &8x & = &11\\\Leftrightarrow & \color{red}{8}x & = &11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+15}& = &12 \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-14}& = &8 \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14} & = &8\color{blue}{+14} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-14}& = &-7 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &-7\color{blue}{+14} \\\Leftrightarrow &-3x & = &7\\\Leftrightarrow & \color{red}{-3}x & = &7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = &-5 \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7} & = &-5\color{blue}{+7} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+6}& = &-11 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-11\color{blue}{-6} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)