Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+5}& = &-2 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &-2\color{blue}{-5} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-11}& = &10 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &10\color{blue}{+11} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-14}& = &-6 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14} & = &-6\color{blue}{+14} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-6}& = &6 \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6} & = &6\color{blue}{+6} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+12}& = &9 \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-4}& = &-14 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = &7 \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+12}& = &3 \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12} & = &3\color{blue}{-12} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-4}& = &-5 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &-5\color{blue}{+4} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-14}& = &-5 \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+15}& = &3 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+10}& = &-9 \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)