Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-10}& = &-7 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-7\color{blue}{+10} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-2}& = &10 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &10\color{blue}{+2} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+9}& = &-8 \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9} & = &-8\color{blue}{-9} \\\Leftrightarrow &6x & = &-17\\\Leftrightarrow & \color{red}{6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+13}& = &-2 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+15}& = &-11 \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &-12x & = &-26\\\Leftrightarrow & \color{red}{-12}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+5}& = &-9 \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5} & = &-9\color{blue}{-5} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-6}& = &8 \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6} & = &8\color{blue}{+6} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+3}& = &-7 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &-7\color{blue}{-3} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-12}& = &10 \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12} & = &10\color{blue}{+12} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+5}& = &8 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = &7 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &7\color{blue}{+4} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = &2 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)