Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+8}& = &10 \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+1}& = &-2 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &-2\color{blue}{-1} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+10}& = &-11 \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-2x & = &-21\\\Leftrightarrow & \color{red}{-2}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-1}& = &2 \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1} & = &2\color{blue}{+1} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-8}& = &5 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &12x & = &13\\\Leftrightarrow & \color{red}{12}x & = &13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-1}& = &-9 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &-9\color{blue}{+1} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-13}& = &-5 \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13} & = &-5\color{blue}{+13} \\\Leftrightarrow &10x & = &8\\\Leftrightarrow & \color{red}{10}x & = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-11}& = &11 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &11\color{blue}{+11} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+8}& = &6 \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8} & = &6\color{blue}{-8} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-1}& = &5 \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-14}& = &4 \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &-12x & = &18\\\Leftrightarrow & \color{red}{-12}x & = &18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+8}& = &-8 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-8\color{blue}{-8} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)