Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+2}& = &-8 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &-8\color{blue}{-2} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-3}& = &8 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-7}& = &-11 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &-11\color{blue}{+7} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-1}& = &6 \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-2}& = &15 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &15\color{blue}{+2} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+2}& = &12 \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2} & = &12\color{blue}{-2} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-10}& = &1 \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10} & = &1\color{blue}{+10} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+6}& = &-15 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-6}& = &-14 \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-10}& = &15 \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+12}& = &-10 \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12} & = &-10\color{blue}{-12} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+11}& = &-5 \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)