Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+8}& = &15 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &15\color{blue}{-8} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-1}& = &-10 \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1} & = &-10\color{blue}{+1} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-1}& = &-12 \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1} & = &-12\color{blue}{+1} \\\Leftrightarrow &2x & = &-11\\\Leftrightarrow & \color{red}{2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+10}& = &12 \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-3}& = &8 \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &4x & = &11\\\Leftrightarrow & \color{red}{4}x & = &11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-15}& = &-10 \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15} & = &-10\color{blue}{+15} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-6}& = &13 \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-14}& = &10 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &10\color{blue}{+14} \\\Leftrightarrow &-5x & = &24\\\Leftrightarrow & \color{red}{-5}x & = &24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+7}& = &-6 \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+10}& = &-12 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &-12\color{blue}{-10} \\\Leftrightarrow &14x & = &-22\\\Leftrightarrow & \color{red}{14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-4}& = &10 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-3}& = &7 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)