Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+10}& = &12 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+5}& = &-8 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &-2x & = &-13\\\Leftrightarrow & \color{red}{-2}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+2}& = &10 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &10\color{blue}{-2} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+3}& = &-1 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-7}& = &-2 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-2}& = &12 \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2} & = &12\color{blue}{+2} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-14}& = &-3 \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14} & = &-3\color{blue}{+14} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+12}& = &9 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+2}& = &13 \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2} & = &13\color{blue}{-2} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-2}& = &11 \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2} & = &11\color{blue}{+2} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-14}& = &14 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &14\color{blue}{+14} \\\Leftrightarrow &8x & = &28\\\Leftrightarrow & \color{red}{8}x & = &28\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{28}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+12}& = &9 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &9\color{blue}{-12} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)